Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
484 conjugacy classes of subgroups; only the 103 normal subgroups are shown.
This group has 484 conjugacy classes of subgroups — too many to draw. Only its 103 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. #26029023 | C2 | semidirect |
| 3. #26021981 | C2 | semidirect |
| 4. #26021141 | C2 | semidirect |
| 5. #26018368 | C2 | semidirect |
| 6. #26018333 | C2 | semidirect |
| 7. C89×#2145 | C2 | semidirect |
| 10. #19152039 | C4 | semidirect |
| 12. #19152034 | C4 | semidirect |
| 50. #15667952 | C2×C4 | semidirect |
| 66. C2×Q16×C89 | C2×C4 | semidirect |
| 68. C2×D8×C89 | C2×C4 | semidirect |
| 194. #2145 | D89 | semidirect |
| 199. C89 | #13027 | semidirect |
| 232. C2×Q16 | C4×D89 | semidirect |
| 236. C2×D8 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26033386 | 2 |
| #26029023 | 2 |
| #26021981 | 2 |
| #26021141 | 2 |
| #26018368 | 2 |
| #26018333 | 2 |
| C89×#2145 | 2 |
| #13027 | 89 |