Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
228 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 59 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 |
|---|---|---|
| 1. Q8×Dic178 | C2 | semidirect |
| 5. #19151346 | C2 | semidirect |
| 6. #19151330 | C2 | semidirect |
| 7. Q8⋊C8×C89 | C2 | semidirect |
| 52. Q8×C89 | SD16 | semidirect |
| 69. Dic178 | SD16 | semidirect |
| 92. C89 | #1623 | semidirect |
| 99. Q8⋊C8 | D89 | semidirect |
| 148. Q8 | #13083563 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic178 | 2 |
| #19151971 | 2 |
| #19151799 | 2 |
| #19151798 | 2 |
| #19151346 | 2 |
| #19151330 | 2 |
| Q8⋊C8×C89 | 2 |
| #1623 | 89 |