Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
492 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 109 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. #21448567 | C2 | semidirect |
| 4. #21444499 | C2 | semidirect |
| 6. #21443678 | C2 | semidirect |
| 7. C61×#1274 | C2 | semidirect |
| 10. #16840135 | C4 | semidirect |
| 11. #16840113 | C4 | semidirect |
| 92. C42×C61 | SD16 | semidirect |
| 183. #1274 | D61 | semidirect |
| 209. C61 | #9301 | semidirect |
| 291. C42 | #11758190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456746 | 2 |
| #21448567 | 2 |
| #21446651 | 2 |
| #21444499 | 2 |
| #21444380 | 2 |
| #21443678 | 2 |
| C61×#1274 | 2 |
| #9301 | 61 |