Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
494 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 494 conjugacy classes of subgroups — too many to draw. Only its 175 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×Dic356 | C2 | semidirect |
| 3. #26022534 | C2 | semidirect |
| 5. #26022395 | C2 | semidirect |
| 7. Q8×C16×C89 | C2 | semidirect |
| 34. #15667957 | Q8 | direct (N × H) |
| 53. Dic356 | C2×Q8 | semidirect |
| 69. C16×C89 | C2×Q8 | semidirect |
| 71. Q8×C89 | SD32 | semidirect |
| 109. Q8×C16 | D89 | semidirect |
| 111. C89 | Q8×SD32 | semidirect |
| 173. C16 | Q8×D89 | semidirect |
| 179. Q8 | #15667957 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic356 | 2 |
| Q8×D712 | 2 |
| #26022534 | 2 |
| #26022400 | 2 |
| #26022395 | 2 |
| C4×#15667957 | 2 |
| Q8×C16×C89 | 2 |
| Q8×SD32 | 89 |