Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
840 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 840 conjugacy classes of subgroups — too many to draw. Only its 97 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. #26022604 | C2 | semidirect |
| 3. #26018769 | C2 | semidirect |
| 4. #26018767 | C2 | semidirect |
| 5. #26018578 | C2 | semidirect |
| 6. #26018138 | C2 | semidirect |
| 7. C89×#1297 | C2 | semidirect |
| 14. #19151535 | C4 | semidirect |
| 15. #19151508 | C4 | semidirect |
| 29. C22×D356 | C2×C4 | semidirect |
| 41. C2×C4⋊Dic89 | C2×C4 | semidirect |
| 59. #15667919 | D4 | semidirect |
| 68. #95×C89 | C2×C4 | semidirect |
| 69. #95×C89 | D4 | semidirect |
| 235. #1297 | D89 | semidirect |
| 236. C89 | #9409 | semidirect |
| 297. #95 | C4×D89 | semidirect |
| 298. #95 | D356 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26025178 | 2 |
| #26022604 | 2 |
| #26018769 | 2 |
| #26018767 | 2 |
| #26018578 | 2 |
| #26018138 | 2 |
| C89×#1297 | 2 |
| #9409 | 89 |