Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
542 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 542 conjugacy classes of subgroups — too many to draw. Only its 99 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 |
|---|---|---|
| 3. #26030774 | C2 | semidirect |
| 5. #26018815 | C2 | semidirect |
| 6. #26018096 | C2 | semidirect |
| 7. C89×#1518 | C2 | semidirect |
| 94. C2×#10623494 | SD16 | semidirect |
| 192. #1518 | D89 | semidirect |
| 194. C89 | #10220 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26031195 | 2 |
| #26031190 | 2 |
| #26030774 | 2 |
| #26021075 | 2 |
| #26018815 | 2 |
| #26018096 | 2 |
| C89×#1518 | 2 |
| #10220 | 89 |