Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
1640 conjugacy classes of subgroups; only the 565 normal subgroups are shown.
This group has 1640 conjugacy classes of subgroups — too many to draw. Only its 565 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×C4⋊C4×C23 | C2 |
| socle | C23×C23 | C24 |
| hypercenter | C22×C4⋊C4 | D23 |
| hypocenter | C23 | C2×#537 |
| LCS | G ▷ C22×C23 ▷ C23 | |
| UCS | C1 ◁ C23 ◁ C22×C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#67288 | C2 | semidirect |
| 2. #13092998 | C2 | direct (N × H) |
| 3. C2×#10625068 | C2 | semidirect |
| 4. C2×#10625066 | C2 | semidirect |
| 5. C2×#10625101 | C2 | semidirect |
| 6. C22×C4⋊C4×C23 | C2 | semidirect |
| 11. C2×#67288 | C22 | semidirect |
| 17. C2×C4⋊C4×C23 | C22 | semidirect |
| 18. #10625101 | C22 | semidirect |
| 21. #10625068 | C22 | semidirect |
| 22. #10625066 | C22 | semidirect |
| 26. C22×C4×C23 | D4 | semidirect |
| 58. C2×C4×C23 | C2×D4 | semidirect |
| 89. C22×C4⋊C4 | D23 | semidirect |
| 91. C2×C23 | #537 | semidirect |
| 110. C2×C4⋊C4 | C2×D23 | semidirect |
| 112. C23 | C2×#537 | semidirect |
| 128. C22×C4 | D92 | semidirect |
| 155. C2×C4 | C2×D92 | semidirect |
| 175. C2 | #13092998 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#67288 | 2 |
| #13092998 | 2 |
| C2×#10625068 | 2 |
| C2×#10625066 | 2 |
| C2×#10625101 | 2 |
| C22×C4⋊C4×C23 | 2 |
| C2×#537 | 23 |