Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
802 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 802 conjugacy classes of subgroups — too many to draw. Only its 127 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. #26018938 | C2 | semidirect |
| 3. #26018676 | C2 | semidirect |
| 4. #26018573 | C2 | semidirect |
| 5. C89×#1800 | C2 | semidirect |
| 173. #1800 | D89 | semidirect |
| 177. C89 | #8397 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152313 | 2 |
| #26018938 | 2 |
| #26018676 | 2 |
| #26018573 | 2 |
| C89×#1800 | 2 |
| #8397 | 89 |