Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1728 conjugacy classes of subgroups; only the 557 normal subgroups are shown.
This group has 1728 conjugacy classes of subgroups — too many to draw. Only its 557 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 | C2×C23×#127 | C2 |
| socle | C23×C23 | C24 |
| hypercenter | C2×#127 | D23 |
| hypocenter | C23 | C2×#532 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C2×#127 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67290 | C2 | semidirect |
| 2. #13092965 | C2 | direct (N × H) |
| 3. C2×#10625040 | C2 | semidirect |
| 4. C2×#10625107 | C2 | semidirect |
| 5. C2×#10625109 | C2 | semidirect |
| 6. C2×D4×Dic23 | C2 | semidirect |
| 7. C2×C42×D23 | C2 | semidirect |
| 8. C2×C23×#127 | C2 | semidirect |
| 14. C2×#67290 | C22 | semidirect |
| 18. C23×#127 | C22 | semidirect |
| 21. #10625109 | C22 | semidirect |
| 22. #10625107 | C22 | semidirect |
| 23. D4×Dic23 | C22 | semidirect |
| 27. C42×D23 | C22 | semidirect |
| 28. #10625040 | C22 | semidirect |
| 46. C2×C4×D23 | D4 | semidirect |
| 66. C2×C4×C23 | #41 | semidirect |
| 78. C4×D23 | C2×D4 | semidirect |
| 91. C4×C23 | C2×#41 | semidirect |
| 98. C2×#127 | D23 | semidirect |
| 104. C2×C23 | #532 | semidirect |
| 118. #127 | C2×D23 | semidirect |
| 128. C23 | C2×#532 | semidirect |
| 177. C2×C4 | #67290 | semidirect |
| 193. C4 | C2×#67290 | semidirect |
| 196. C2 | #13092965 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67290 | 2 |
| #13092965 | 2 |
| C2×#10625040 | 2 |
| C2×#10625107 | 2 |
| C2×#10625109 | 2 |
| C2×D4×Dic23 | 2 |
| C2×C42×D23 | 2 |
| C2×C23×#127 | 2 |
| C2×#532 | 23 |