Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
558 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 558 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. #21454538 | C2 | semidirect |
| 3. #21446643 | C2 | semidirect |
| 4. #21444486 | C2 | semidirect |
| 5. #21444380 | C2 | semidirect |
| 6. #21443678 | C2 | semidirect |
| 7. C61×#1275 | C2 | semidirect |
| 11. #16840139 | C4 | semidirect |
| 12. #16840109 | C4 | semidirect |
| 102. C2×C8×C61 | D8 | semidirect |
| 195. #1275 | D61 | semidirect |
| 222. C61 | #9293 | semidirect |
| 304. C2×C8 | D488 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456739 | 2 |
| #21454538 | 2 |
| #21446643 | 2 |
| #21444486 | 2 |
| #21444380 | 2 |
| #21443678 | 2 |
| C61×#1275 | 2 |
| #9293 | 61 |