Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. C2×#19152036 | C2 | semidirect |
| 2. C2×#19151869 | C2 | semidirect |
| 3. #26029924 | C2 | semidirect |
| 4. C2×#19151404 | C2 | semidirect |
| 5. C2×#19151398 | C2 | semidirect |
| 6. C2×#19151383 | C2 | semidirect |
| 7. C89×#1387 | C2 | semidirect |
| 50. C2×D712 | D4 | semidirect |
| 75. M32×C89 | D4 | semidirect |
| 78. #108×C89 | D4 | semidirect |
| 225. #1387 | D89 | semidirect |
| 226. C89 | #13307 | semidirect |
| 288. M32 | D356 | semidirect |
| 294. #108 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| C2×#19151869 | 2 |
| #26029924 | 2 |
| C2×#19151404 | 2 |
| C2×#19151398 | 2 |
| C2×#19151383 | 2 |
| C89×#1387 | 2 |
| #13307 | 89 |