Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
334 conjugacy classes of subgroups; only the 83 normal subgroups are shown.
This group has 334 conjugacy classes of subgroups — too many to draw. Only its 83 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. #19151608 | C2 | semidirect |
| 5. #19151503 | C2 | semidirect |
| 6. #19151359 | C2 | semidirect |
| 7. #343×C89 | C2 | semidirect |
| 11. #15668045 | C4 | semidirect |
| 37. C2×Dic178 | C2×C4 | semidirect |
| 61. M16×C89 | C2×C4 | semidirect |
| 125. C89 | #1882 | semidirect |
| 131. #343 | D89 | semidirect |
| 177. M16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15668045 | 2 |
| #19152079 | 2 |
| C2×#15667938 | 2 |
| #19151608 | 2 |
| #19151503 | 2 |
| #19151359 | 2 |
| #343×C89 | 2 |
| #1882 | 89 |