Finite Group DatabasebetaFinite Group DatabasebetaOrder 22592.
152 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 43 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 |
|---|---|---|
| 2. C2×#19150727 | C2 | semidirect |
| 3. C2×#19150726 | C2 | semidirect |
| 4. #26014972 | C2 | semidirect |
| 5. #26014912 | C2 | semidirect |
| 6. #26014904 | C2 | semidirect |
| 7. #103×C353 | C2 | semidirect |
| 60. C353 | #452 | semidirect |
| 66. #103 | D353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#19150738 | 2 |
| C2×#19150727 | 2 |
| C2×#19150726 | 2 |
| #26014972 | 2 |
| #26014912 | 2 |
| #26014904 | 2 |
| #103×C353 | 2 |
| #452 | 353 |