Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1174 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 1174 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. #26031049 | C2 | semidirect |
| 2. #26023885 | C2 | semidirect |
| 3. #26020173 | C2 | semidirect |
| 4. #26018768 | C2 | semidirect |
| 5. #26018767 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#2433 | C2 | semidirect |
| 31. C22×D356 | D4 | semidirect |
| 36. C2×#13083558 | D4 | semidirect |
| 43. C2×C4⋊Dic89 | D4 | semidirect |
| 56. #15667919 | D4 | semidirect |
| 67. C22×D4×C89 | D4 | semidirect |
| 75. C2×C4⋊C4×C89 | D4 | semidirect |
| 80. #95×C89 | D4 | semidirect |
| 263. #2433 | D89 | semidirect |
| 268. C89 | #10326 | semidirect |
| 305. C22×D4 | C22⋊D89 | semidirect |
| 323. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 341. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031049 | 2 |
| #26023885 | 2 |
| #26020173 | 2 |
| #26018768 | 2 |
| #26018767 | 2 |
| #26018138 | 2 |
| C89×#2433 | 2 |
| #10326 | 89 |