Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
372 conjugacy classes of subgroups; only the 55 normal subgroups are shown.
This group has 372 conjugacy classes of subgroups — too many to draw. Only its 55 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. #26021414 | C2 | semidirect |
| 3. #26019228 | C2 | semidirect |
| 5. #26018281 | C2 | semidirect |
| 6. #26018185 | C2 | semidirect |
| 188. C89 | #12275 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26028423 | 2 |
| #26021414 | 2 |
| #26019228 | 2 |
| #26019191 | 2 |
| #26018281 | 2 |
| #26018185 | 2 |
| C89×#1345 | 2 |
| #12275 | 89 |