Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
548 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 548 conjugacy classes of subgroups — too many to draw. Only its 113 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×#19151645 | C2 | semidirect |
| 3. C2×#19151412 | C2 | semidirect |
| 4. C2×#19151410 | C2 | semidirect |
| 5. C2×#19151379 | C2 | semidirect |
| 6. #26018350 | C2 | semidirect |
| 7. C89×#1383 | C2 | semidirect |
| 54. #15667948 | D4 | semidirect |
| 64. #108×C89 | D4 | semidirect |
| 185. #1383 | D89 | semidirect |
| 186. C89 | #13010 | semidirect |
| 242. #108 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19151852 | 2 |
| C2×#19151645 | 2 |
| C2×#19151412 | 2 |
| C2×#19151410 | 2 |
| C2×#19151379 | 2 |
| #26018350 | 2 |
| C89×#1383 | 2 |
| #13010 | 89 |