Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
554 conjugacy classes of subgroups; only the 131 normal subgroups are shown.
This group has 554 conjugacy classes of subgroups — too many to draw. Only its 131 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. #21446646 | C2 | semidirect |
| 3. C4×C8×Dic61 | C2 | semidirect |
| 4. #21444269 | C2 | semidirect |
| 5. C61×#1567 | C2 | semidirect |
| 7. #16840167 | C4 | semidirect |
| 8. #16840139 | C4 | semidirect |
| 9. #16840109 | C4 | semidirect |
| 75. C4×Dic61 | D8 | semidirect |
| 104. C8×C61 | #104 | semidirect |
| 126. #1567 | D61 | semidirect |
| 147. C61 | #9844 | semidirect |
| 233. C8 | #14519703 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456398 | 2 |
| #21446646 | 2 |
| C4×C8×Dic61 | 2 |
| #21444269 | 2 |
| C61×#1567 | 2 |
| #9844 | 61 |