Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
998 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 998 conjugacy classes of subgroups — too many to draw. Only its 117 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. C4×#15667928 | C2 | semidirect |
| 3. #26018850 | C2 | semidirect |
| 4. #26018700 | C2 | semidirect |
| 5. #26018698 | C2 | semidirect |
| 6. #26018592 | C2 | semidirect |
| 7. C89×#1527 | C2 | semidirect |
| 233. Dic178 | #100 | semidirect |
| 281. #1527 | D89 | semidirect |
| 285. C89 | #8369 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152256 | 2 |
| C4×#15667928 | 2 |
| #26018850 | 2 |
| #26018700 | 2 |
| #26018698 | 2 |
| #26018592 | 2 |
| C89×#1527 | 2 |
| #8369 | 89 |