Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1066 conjugacy classes of subgroups; only the 122 normal subgroups are shown.
This group has 1066 conjugacy classes of subgroups — too many to draw. Only its 122 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C61 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C61 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C23×C4×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3186 | C2 | semidirect |
| 2. C61×#2847 | C2 | semidirect |
| 3. C61×#1779 | C2 | semidirect |
| 4. C61×#1519 | C2 | semidirect |
| 5. C61×#1289 | C2 | semidirect |
| 24. C22×D4×C61 | D4 | semidirect |
| 34. C22×C8×C61 | D4 | semidirect |
| 43. C2×C4⋊C4×C61 | D4 | semidirect |
| 54. #95×C61 | D4 | semidirect |
| 62. C24×C61 | D8 | semidirect |
| 169. #10320 | C61 | direct (N × H) |
| 204. #3186 | C2×C61 | semidirect |
| 205. #2847 | C2×C61 | semidirect |
| 206. #1779 | C2×C61 | semidirect |
| 207. #1519 | C2×C61 | semidirect |
| 208. #1289 | C2×C61 | semidirect |
| 233. C61 | #10320 | direct (N × H) |
| 237. C22×D4 | D4×C61 | semidirect |
| 247. C22×C8 | D4×C61 | semidirect |
| 256. C2×C4⋊C4 | D4×C61 | semidirect |
| 267. #95 | D4×C61 | semidirect |
| 275. C24 | D8×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3186 | 2 |
| C61×#2847 | 2 |
| C61×#1779 | 2 |
| C61×#1519 | 2 |
| C61×#1289 | 2 |
| #10320 | 61 |