Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
822 conjugacy classes of subgroups; only the 81 normal subgroups are shown.
This group has 822 conjugacy classes of subgroups — too many to draw. Only its 81 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. #26029504 | C2 | semidirect |
| 2. #26028274 | C2 | semidirect |
| 3. #26020170 | C2 | semidirect |
| 4. #26018782 | C2 | semidirect |
| 5. #26018781 | C2 | semidirect |
| 6. #26018161 | C2 | semidirect |
| 7. C89×#3006 | C2 | semidirect |
| 54. C22⋊#10623494 | D4 | semidirect |
| 65. C22×Q8×C89 | D4 | semidirect |
| 69. C22×D4×C89 | D4 | semidirect |
| 85. C22⋊C8×C89 | D4 | semidirect |
| 272. #3006 | D89 | semidirect |
| 278. C89 | #9980 | semidirect |
| 309. C22×Q8 | C22⋊D89 | semidirect |
| 316. C22×D4 | C22⋊D89 | semidirect |
| 351. C22⋊C8 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029504 | 2 |
| #26028274 | 2 |
| #26020170 | 2 |
| #26018782 | 2 |
| #26018781 | 2 |
| #26018161 | 2 |
| C89×#3006 | 2 |
| #9980 | 89 |