Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
402 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 402 conjugacy classes of subgroups — too many to draw. Only its 109 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. C2×#19151426 | C2 | semidirect |
| 5. #26021037 | C2 | semidirect |
| 6. #26018361 | C2 | semidirect |
| 7. C89×#1379 | C2 | semidirect |
| 19. #19151406 | C4 | semidirect |
| 43. #15667948 | C2×C4 | semidirect |
| 60. C2×C16×C89 | C2×C4 | semidirect |
| 166. #1379 | D89 | semidirect |
| 167. C89 | #12946 | semidirect |
| 210. C2×C16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029129 | 2 |
| C2×#19151426 | 2 |
| C2×#19151406 | 2 |
| #26021965 | 2 |
| #26021037 | 2 |
| #26018361 | 2 |
| C89×#1379 | 2 |
| #12946 | 89 |