Finite Group DatabasebetaFinite Group DatabasebetaOrder 2944.
152 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #13092241 | C2 | semidirect |
| 5. #13092240 | C2 | semidirect |
| 6. #13092239 | C2 | semidirect |
| 7. C23×#365 | C2 | semidirect |
| 19. #10624980 | C4 | semidirect |
| 20. C16×D23 | C4 | semidirect |
| 36. C16×C23 | C2×C4 | semidirect |
| 37. C23⋊C16 | C2×C4 | semidirect |
| 71. #365 | D23 | direct (N × H) |
| 75. D23 | #365 | direct (N × H) |
| 89. C23 | C2×#365 | semidirect |
| 106. C16 | C4×D23 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| M32×D23 | 2 |
| #108×D23 | 2 |
| #106×D23 | 2 |
| #13092241 | 2 |
| #13092240 | 2 |
| #13092239 | 2 |
| C23×#365 | 2 |
| C2×#365 | 23 |