Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
228 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 105 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. #26014990 | C2 | semidirect |
| 2. #26014982 | C2 | semidirect |
| 3. #26014982 | C2 | semidirect |
| 4. #26014970 | C2 | semidirect |
| 5. #26014970 | C2 | semidirect |
| 6. #26014969 | C2 | semidirect |
| 7. #26014969 | C2 | semidirect |
| 8. #26014968 | C2 | semidirect |
| 9. #26014957 | C2 | semidirect |
| 13. C2×#19150716 | C2 | semidirect |
| 14. C4⋊C4×D353 | C2 | semidirect |
| 15. C22⋊Q8×C353 | C2 | semidirect |
| 54. C22⋊D353 | Q8 | semidirect |
| 101. C353 | #554 | semidirect |
| 111. C22⋊Q8 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26014990 | 2 |
| #26014982 | 2 |
| #26014970 | 2 |
| #26014969 | 2 |
| #26014968 | 2 |
| #26014957 | 2 |
| C4×C22⋊D353 | 2 |
| #26014952 | 2 |
| C2×#19150716 | 2 |
| C4⋊C4×D353 | 2 |
| C22⋊Q8×C353 | 2 |
| #554 | 353 |