Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
124 conjugacy classes of subgroups; only the 45 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 45 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×#19150724 | C2 | semidirect |
| 2. C22×#15667725 | C2 | semidirect |
| 4. #26014923 | C2 | semidirect |
| 5. #26014916 | C2 | semidirect |
| 6. #26014912 | C2 | semidirect |
| 7. C22⋊Q8×C353 | C2 | semidirect |
| 27. #15667725 | D4 | semidirect |
| 39. C22×C353 | SD16 | semidirect |
| 55. C353 | #465 | semidirect |
| 59. C22⋊Q8 | D353 | semidirect |
| 98. C22 | #19150724 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150724 | 2 |
| C22×#15667725 | 2 |
| #26014966 | 2 |
| #26014923 | 2 |
| #26014916 | 2 |
| #26014912 | 2 |
| C22⋊Q8×C353 | 2 |
| #465 | 353 |