Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
496 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 4. #26021168 | C2 | semidirect |
| 5. #26018347 | C2 | semidirect |
| 6. #26018342 | C2 | semidirect |
| 7. C89×#2141 | C2 | semidirect |
| 12. C2×#15667955 | C4 | semidirect |
| 42. C2×#13083549 | C2×C4 | semidirect |
| 56. C2×Q16×C89 | C2×C4 | semidirect |
| 164. #2141 | D89 | semidirect |
| 168. C89 | #13019 | semidirect |
| 194. C2×Q16 | C4×D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15667955 | 2 |
| #26029103 | 2 |
| C2×#19151412 | 2 |
| #26021168 | 2 |
| #26018347 | 2 |
| #26018342 | 2 |
| C89×#2141 | 2 |
| #13019 | 89 |