Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #21456734 | C2 | semidirect |
| 2. #21450765 | C2 | semidirect |
| 3. #21444488 | C2 | semidirect |
| 4. #21444314 | C2 | semidirect |
| 5. #21444210 | C2 | semidirect |
| 6. #21443720 | C2 | semidirect |
| 7. C61×#3036 | C2 | semidirect |
| 47. C4⋊#92418 | D4 | semidirect |
| 62. C4⋊Q8×C61 | D4 | semidirect |
| 63. #127×C61 | D4 | semidirect |
| 77. C4⋊C8×C61 | D4 | semidirect |
| 96. C2×D4×C61 | D8 | semidirect |
| 234. #3036 | D61 | semidirect |
| 271. C61 | #10238 | semidirect |
| 285. C4⋊Q8 | C22⋊D61 | semidirect |
| 292. #127 | C22⋊D61 | semidirect |
| 312. C4⋊C8 | C22⋊D61 | semidirect |
| 352. C2×D4 | #11758199 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #21456734 | 2 |
| #21450765 | 2 |
| #21444488 | 2 |
| #21444314 | 2 |
| #21444210 | 2 |
| #21443720 | 2 |
| C61×#3036 | 2 |
| #10238 | 61 |