Finite Group DatabasebetaFinite Group DatabasebetaOrder 11392.
374 conjugacy classes of subgroups; only the 133 normal subgroups are shown.
This group has 374 conjugacy classes of subgroups — too many to draw. Only its 133 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. #19152305 | C2 | semidirect |
| 2. D4×Dic178 | C2 | semidirect |
| 3. #19152006 | C2 | semidirect |
| 4. #19151996 | C2 | semidirect |
| 5. #19151900 | C2 | semidirect |
| 6. #19151888 | C2 | semidirect |
| 7. #19151886 | C2 | semidirect |
| 8. #19151878 | C2 | semidirect |
| 9. #19151728 | C2 | semidirect |
| 65. D8×C89 | Q8 | semidirect |
| 78. D4×C89 | C2×Q8 | semidirect |
| 97. C8×C89 | C2×Q8 | semidirect |
| 122. C89 | #3384 | semidirect |
| 174. D8 | Dic178 | semidirect |
| 204. D4 | C2×Dic178 | semidirect |
| 220. C8 | C2×Dic178 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #19152305 | 2 |
| D4×Dic178 | 2 |
| #19152006 | 2 |
| #19151996 | 2 |
| #19151900 | 2 |
| #19151888 | 2 |
| #19151886 | 2 |
| #19151878 | 2 |
| #19151728 | 2 |
| #19151710 | 2 |
| C4×D8×C89 | 2 |
| #3384 | 89 |