Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
514 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 514 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. #26028888 | C2 | semidirect |
| 3. #26018696 | C2 | semidirect |
| 4. #26018694 | C2 | semidirect |
| 5. #26018584 | C2 | semidirect |
| 6. #26018116 | C2 | semidirect |
| 7. C89×#1288 | C2 | semidirect |
| 62. C4×#10623494 | D4 | semidirect |
| 71. C4×C8×C89 | D4 | semidirect |
| 227. #1288 | D89 | semidirect |
| 228. C89 | #9494 | semidirect |
| 290. C4×C8 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028888 | 2 |
| #26025820 | 2 |
| #26018696 | 2 |
| #26018694 | 2 |
| #26018584 | 2 |
| #26018116 | 2 |
| C89×#1288 | 2 |
| #9494 | 89 |