Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
486 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 109 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. #26033354 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. #26020299 | C2 | semidirect |
| 6. #26018368 | C2 | semidirect |
| 7. C89×#1389 | C2 | semidirect |
| 47. #15667952 | D4 | semidirect |
| 60. M32×C89 | D4 | semidirect |
| 175. #1389 | D89 | semidirect |
| 176. C89 | #13079 | semidirect |
| 222. M32 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033354 | 2 |
| #26029901 | 2 |
| C2×#19151412 | 2 |
| C2×#19151410 | 2 |
| #26020299 | 2 |
| #26018368 | 2 |
| C89×#1389 | 2 |
| #13079 | 89 |