Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1736 conjugacy classes of subgroups; only the 573 normal subgroups are shown.
This group has 1736 conjugacy classes of subgroups — too many to draw. Only its 573 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C23 | C23×D23 |
| commutator, cosocle | C22×C23 | C25 |
| Frattini | C22 | C24×D23 |
| Fitting | C22×#41×C23 | C2 |
| socle | C23×C23 | C24 |
| hypercenter | C22×#41 | D23 |
| hypocenter | C23 | C2×#550 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67292 | C2 | semidirect |
| 2. #13093086 | C2 | direct (N × H) |
| 3. C2×#10625111 | C2 | semidirect |
| 4. C2×#10625101 | C2 | semidirect |
| 5. C2×#10625109 | C2 | semidirect |
| 6. C2×Q8×Dic23 | C2 | semidirect |
| 7. C2×C4×C22⋊D23 | C2 | semidirect |
| 8. C22×#41×C23 | C2 | semidirect |
| 10. C2×#41×C23 | C22 | semidirect |
| 17. C2×#67292 | C22 | semidirect |
| 21. Q8×Dic23 | C22 | semidirect |
| 22. #10625111 | C22 | semidirect |
| 23. #10625109 | C22 | semidirect |
| 24. #10625101 | C22 | semidirect |
| 25. C4×C22⋊D23 | C22 | semidirect |
| 33. C2×Q8×C23 | D4 | semidirect |
| 67. Q8×C23 | C2×D4 | semidirect |
| 78. C2×Dic23 | #41 | semidirect |
| 101. Dic23 | C2×#41 | semidirect |
| 103. C22×#41 | D23 | semidirect |
| 111. C2×C23 | #550 | semidirect |
| 119. C2×#41 | C2×D23 | semidirect |
| 137. C23 | C2×#550 | semidirect |
| 142. C2×Q8 | C22⋊D23 | semidirect |
| 175. Q8 | C2×C22⋊D23 | semidirect |
| 211. C2 | #13093086 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67292 | 2 |
| #13093086 | 2 |
| C2×#10625111 | 2 |
| C2×#10625101 | 2 |
| C2×#10625109 | 2 |
| C2×Q8×Dic23 | 2 |
| C2×C4×C22⋊D23 | 2 |
| C22×#41×C23 | 2 |
| C2×#550 | 23 |