Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
408 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 408 conjugacy classes of subgroups — too many to draw. Only its 93 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. C2×#19151406 | C2 | semidirect |
| 3. #26021962 | C2 | semidirect |
| 4. C2×#19151381 | C2 | semidirect |
| 5. #26020317 | C2 | semidirect |
| 6. #26018360 | C2 | semidirect |
| 7. C2×#367×C89 | C2 | semidirect |
| 63. C2×C16×C89 | D4 | semidirect |
| 185. C2×#367 | D89 | semidirect |
| 191. C89 | #13385 | semidirect |
| 241. C2×C16 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26029924 | 2 |
| C2×#19151406 | 2 |
| #26021962 | 2 |
| C2×#19151381 | 2 |
| #26020317 | 2 |
| #26018360 | 2 |
| C2×#367×C89 | 2 |
| #13385 | 89 |