Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1044 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1044 conjugacy classes of subgroups — too many to draw. Only its 89 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. #26031054 | C2 | semidirect |
| 3. #26020173 | C2 | semidirect |
| 4. #26018772 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#2435 | C2 | semidirect |
| 36. C2×#13083558 | D4 | semidirect |
| 58. C22×Q8×C89 | D4 | semidirect |
| 73. C2×C4⋊C4×C89 | D4 | semidirect |
| 79. #95×C89 | D4 | semidirect |
| 249. #2435 | D89 | semidirect |
| 255. C89 | #10329 | semidirect |
| 280. C22×Q8 | C22⋊D89 | semidirect |
| 308. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 327. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031054 | 2 |
| #26023885 | 2 |
| #26020173 | 2 |
| #26018772 | 2 |
| #26018767 | 2 |
| #26018138 | 2 |
| C89×#2435 | 2 |
| #10329 | 89 |