Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
124 conjugacy classes of subgroups; only the 41 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 41 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 |
| 3. C4×D1412 | C2 | semidirect |
| 4. C4⋊#15667725 | C2 | semidirect |
| 5. #26014916 | C2 | semidirect |
| 6. #26014913 | C2 | semidirect |
| 7. #124×C353 | C2 | semidirect |
| 55. C353 | #463 | semidirect |
| 59. #124 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150724 | 2 |
| C2×#19150722 | 2 |
| C4×D1412 | 2 |
| C4⋊#15667725 | 2 |
| #26014916 | 2 |
| #26014913 | 2 |
| #124×C353 | 2 |
| #463 | 353 |