Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
1170 conjugacy classes of subgroups; only the 167 normal subgroups are shown.
This group has 1170 conjugacy classes of subgroups — too many to draw. Only its 167 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 |
|---|---|---|
| 1. C2×#19152229 | C2 | semidirect |
| 3. #26019225 | C2 | semidirect |
| 4. #26019191 | C2 | semidirect |
| 5. #26018784 | C2 | semidirect |
| 6. #26018582 | C2 | semidirect |
| 181. C2×C4×C89 | #137 | semidirect |
| 230. C89 | #18143 | semidirect |
| 411. C2×C4 | #15668042 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19152229 | 2 |
| #26029512 | 2 |
| #26019225 | 2 |
| #26019191 | 2 |
| #26018784 | 2 |
| #26018582 | 2 |
| C89×#2406 | 2 |
| #18143 | 89 |