Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
5134 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 5134 conjugacy classes of subgroups — too many to draw. Only its 494 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C61 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C61 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#127×C61 | C2 | semidirect |
| 2. C22×#120×C61 | C2 | semidirect |
| 3. C2×C61×#392 | C2 | semidirect |
| 4. C61×#1438 | C2 | semidirect |
| 5. C61×#1437 | C2 | semidirect |
| 9. C23×D4×C61 | C22 | semidirect |
| 15. C22×C22⋊C4×C61 | C22 | semidirect |
| 16. C22×C42×C61 | C22 | semidirect |
| 18. C2×#95×C61 | C22 | semidirect |
| 37. C22×D4×C61 | D4 | semidirect |
| 48. C2×C22⋊C4×C61 | D4 | semidirect |
| 134. C23×C61 | #127 | semidirect |
| 149. C2×C4×C61 | #120 | semidirect |
| 150. #15258 | C61 | direct (N × H) |
| 175. C22×#127 | C2×C61 | semidirect |
| 176. C22×#120 | C2×C61 | semidirect |
| 177. C2×#392 | C2×C61 | semidirect |
| 178. #1438 | C2×C61 | semidirect |
| 179. #1437 | C2×C61 | semidirect |
| 189. C23×D4 | C22×C61 | semidirect |
| 195. C22×C22⋊C4 | C22×C61 | semidirect |
| 196. C22×C42 | C22×C61 | semidirect |
| 198. C2×#95 | C22×C61 | semidirect |
| 199. C61 | #15258 | direct (N × H) |
| 218. C22×D4 | D4×C61 | semidirect |
| 229. C2×C22⋊C4 | D4×C61 | semidirect |
| 315. C23 | #127×C61 | semidirect |
| 330. C2×C4 | #120×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#127×C61 | 2 |
| C22×#120×C61 | 2 |
| C2×C61×#392 | 2 |
| C61×#1438 | 2 |
| C61×#1437 | 2 |
| #15258 | 61 |