Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
554 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 59 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. #26019237 | C2 | semidirect |
| 3. #26019203 | C2 | semidirect |
| 4. #26018273 | C2 | semidirect |
| 5. #26018252 | C2 | semidirect |
| 6. #26018180 | C2 | semidirect |
| 7. C89×#2736 | C2 | semidirect |
| 45. C22×Q8×C89 | D4 | semidirect |
| 47. C2×C4⋊C4×C89 | D4 | semidirect |
| 63. #95×C89 | D4 | semidirect |
| 64. #95×C89 | D4 | semidirect |
| 231. #2736 | D89 | semidirect |
| 238. C89 | #12188 | semidirect |
| 259. C22×Q8 | C22⋊D89 | semidirect |
| 270. C2×C4⋊C4 | C22⋊D89 | semidirect |
| 294. #95 | C22⋊D89 | semidirect |
| 295. #95 | C22⋊D89 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26021378 | 2 |
| #26019237 | 2 |
| #26019203 | 2 |
| #26018273 | 2 |
| #26018252 | 2 |
| #26018180 | 2 |
| C89×#2736 | 2 |
| #12188 | 89 |