Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
594 conjugacy classes of subgroups; only the 109 normal subgroups are shown.
This group has 594 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 |
|---|---|---|
| 3. #21446800 | C2 | semidirect |
| 5. #21444384 | C2 | semidirect |
| 6. #21443678 | C2 | semidirect |
| 7. C61×#1274 | C2 | semidirect |
| 11. #16840135 | C4 | semidirect |
| 12. #16840109 | C4 | semidirect |
| 33. #14519777 | C2×C4 | semidirect |
| 34. #14519777 | C2×C4 | semidirect |
| 64. C4×C8×C61 | C2×C4 | semidirect |
| 96. C42×C61 | SD16 | semidirect |
| 195. #1274 | D61 | semidirect |
| 221. C61 | #9295 | semidirect |
| 257. C4×C8 | C4×D61 | semidirect |
| 308. C42 | #11758190 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456762 | 2 |
| #21448544 | 2 |
| #21446800 | 2 |
| #21444486 | 2 |
| #21444384 | 2 |
| #21443678 | 2 |
| C61×#1274 | 2 |
| #9295 | 61 |