Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
532 conjugacy classes of subgroups; only the 93 normal subgroups are shown.
This group has 532 conjugacy classes of subgroups — too many to draw. Only its 93 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. #21458953 | C2 | semidirect |
| 2. #21455535 | C2 | semidirect |
| 3. #21455482 | C2 | semidirect |
| 4. #21447548 | C2 | semidirect |
| 5. #21447448 | C2 | semidirect |
| 6. #21443917 | C2 | semidirect |
| 7. C2×C61×#360 | C2 | semidirect |
| 66. C2×#11758185 | D4 | semidirect |
| 68. #14519713 | D4 | semidirect |
| 78. C2×Q16×C61 | D4 | semidirect |
| 80. C2×D8×C61 | D4 | semidirect |
| 223. C2×#360 | D61 | semidirect |
| 259. C61 | #13318 | semidirect |
| 277. C2×Q16 | D244 | semidirect |
| 281. C2×D8 | D244 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21458953 | 2 |
| #21455535 | 2 |
| #21455482 | 2 |
| #21447548 | 2 |
| #21447448 | 2 |
| #21443917 | 2 |
| C2×C61×#360 | 2 |
| #13318 | 61 |