Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
504 conjugacy classes of subgroups; only the 85 normal subgroups are shown.
This group has 504 conjugacy classes of subgroups — too many to draw. Only its 85 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. #26021581 | C2 | semidirect |
| 4. #26021351 | C2 | semidirect |
| 5. #26018074 | C2 | semidirect |
| 7. C89×#1272 | C2 | semidirect |
| 73. C2×D356 | Q16 | semidirect |
| 211. #1272 | D89 | semidirect |
| 214. C89 | #7756 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26027270 | 2 |
| #26021581 | 2 |
| #26021389 | 2 |
| #26021351 | 2 |
| #26018074 | 2 |
| #26018072 | 2 |
| C89×#1272 | 2 |
| #7756 | 89 |