Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1206 conjugacy classes of subgroups; only the 403 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 403 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 |
|---|---|---|
| 2. #26022614 | C2 | semidirect |
| 3. C4×#15667945 | C2 | semidirect |
| 4. #26020080 | C2 | semidirect |
| 5. #26020077 | C2 | semidirect |
| 6. #26019939 | C2 | semidirect |
| 7. C89×#2275 | C2 | semidirect |
| 10. C4×#13083559 | C4 | semidirect |
| 31. C4×D356 | C2×C4 | semidirect |
| 35. #15667945 | C2×C4 | semidirect |
| 36. #15667933 | C2×C4 | semidirect |
| 37. #15667932 | C2×C4 | semidirect |
| 39. C4×#10623494 | C2×C4 | semidirect |
| 44. C4×D4×C89 | C2×C4 | semidirect |
| 58. #13083559 | C42 | semidirect |
| 130. #2275 | D89 | semidirect |
| 135. C89 | #20508 | semidirect |
| 163. C4×D4 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×#13083559 | 2 |
| #26022614 | 2 |
| C4×#15667945 | 2 |
| #26020080 | 2 |
| #26020077 | 2 |
| #26019939 | 2 |
| C89×#2275 | 2 |
| #20508 | 89 |