Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
522 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 522 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 |
|---|---|---|
| 2. #26029054 | C2 | semidirect |
| 3. C2×#19151409 | C2 | semidirect |
| 4. #26021969 | C2 | semidirect |
| 5. #26021128 | C2 | semidirect |
| 6. #26018358 | C2 | semidirect |
| 7. C89×#1377 | C2 | semidirect |
| 12. #19152036 | C4 | semidirect |
| 41. C2×D712 | C2×C4 | semidirect |
| 66. M32×C89 | C2×C4 | semidirect |
| 89. Dic356 | C22⋊C4 | semidirect |
| 97. D712 | C22⋊C4 | semidirect |
| 191. #1377 | D89 | semidirect |
| 192. C89 | #13025 | semidirect |
| 244. M32 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152036 | 2 |
| #26029054 | 2 |
| C2×#19151409 | 2 |
| #26021969 | 2 |
| #26021128 | 2 |
| #26018358 | 2 |
| C89×#1377 | 2 |
| #13025 | 89 |