Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1318 conjugacy classes of subgroups; only the 195 normal subgroups are shown.
This group has 1318 conjugacy classes of subgroups — too many to draw. Only its 195 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×#16840374 | C2 | semidirect |
| 3. #21446965 | C2 | semidirect |
| 4. #21446901 | C2 | semidirect |
| 5. #21446177 | C2 | semidirect |
| 6. #21446131 | C2 | semidirect |
| 7. #21445890 | C2 | semidirect |
| 11. C2×#14519777 | C22 | semidirect |
| 13. C2×#14519769 | C22 | semidirect |
| 16. C2×C4×Dic122 | C22 | semidirect |
| 18. C2×#14519700 | C22 | semidirect |
| 21. #16839524 | C22 | semidirect |
| 22. #16839517 | C22 | semidirect |
| 23. #16839517 | C22 | semidirect |
| 217. C61 | #23942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16840374 | 2 |
| C2×#16839913 | 2 |
| #21446965 | 2 |
| #21446901 | 2 |
| #21446177 | 2 |
| #21446131 | 2 |
| #21445890 | 2 |
| C61×#2309 | 2 |
| #23942 | 61 |