Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
576 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26023409 | C2 | semidirect |
| 2. #26021089 | C2 | semidirect |
| 3. #26018781 | C2 | semidirect |
| 4. #26018768 | C2 | semidirect |
| 5. #26018159 | C2 | semidirect |
| 6. #26018106 | C2 | semidirect |
| 26. #481×C89 | C4 | semidirect |
| 29. #447×C89 | C4 | semidirect |
| 57. C22×D4×C89 | C2×C4 | semidirect |
| 70. C2×C4⋊C4×C89 | C2×C4 | semidirect |
| 78. C22⋊C8×C89 | C2×C4 | semidirect |
| 256. C89 | #9343 | semidirect |
| 260. #481 | Dic89 | semidirect |
| 263. #447 | Dic89 | semidirect |
| 282. C22×D4 | C2×Dic89 | semidirect |
| 299. C2×C4⋊C4 | C2×Dic89 | semidirect |
| 320. C22⋊C8 | C2×Dic89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26023409 | 2 |
| #26021089 | 2 |
| #26018781 | 2 |
| #26018768 | 2 |
| #26018159 | 2 |
| #26018106 | 2 |
| C89×#3192 | 2 |
| #9343 | 89 |