Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
532 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 95 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. #21455535 | C2 | semidirect |
| 2. #21455477 | C2 | semidirect |
| 3. C2×#16839572 | C2 | semidirect |
| 4. #21447547 | C2 | semidirect |
| 5. #21447446 | C2 | semidirect |
| 6. #21443918 | C2 | semidirect |
| 7. C61×#3414 | C2 | semidirect |
| 57. #14519713 | D4 | semidirect |
| 75. C2×Q16×C61 | D4 | semidirect |
| 79. C2×D8×C61 | D4 | semidirect |
| 87. C2×C16×C61 | D4 | semidirect |
| 220. #3414 | D61 | semidirect |
| 259. C61 | #13318 | semidirect |
| 277. C2×Q16 | C22⋊D61 | semidirect |
| 281. C2×D8 | C22⋊D61 | semidirect |
| 306. C2×C16 | C22⋊D61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21455535 | 2 |
| #21455477 | 2 |
| C2×#16839572 | 2 |
| #21447547 | 2 |
| #21447446 | 2 |
| #21443918 | 2 |
| C61×#3414 | 2 |
| #13318 | 61 |