Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
2080 conjugacy classes of subgroups; only the 302 normal subgroups are shown.
This group has 2080 conjugacy classes of subgroups — too many to draw. Only its 302 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C61 | C22×D4 |
| commutator, Frattini, cosocle | C22×C4 | C24×C61 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C61 ◁ C22×#41×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C61×#535 | C2 | semidirect |
| 2. C2×C61×#447 | C2 | semidirect |
| 3. C61×#1999 | C2 | semidirect |
| 4. C61×#1875 | C2 | semidirect |
| 5. C61×#1780 | C2 | semidirect |
| 7. C23×D4×C61 | C22 | semidirect |
| 13. C2×#121×C61 | C22 | semidirect |
| 16. C2×#117×C61 | C22 | semidirect |
| 18. C2×#102×C61 | C22 | semidirect |
| 19. C2×C22⋊C8×C61 | C22 | semidirect |
| 20. C2×C22⋊C8×C61 | C22 | semidirect |
| 21. C61×#340 | C22 | semidirect |
| 45. #121×C61 | D4 | semidirect |
| 139. #23925 | C61 | direct (N × H) |
| 160. C2×#535 | C2×C61 | semidirect |
| 161. C2×#447 | C2×C61 | semidirect |
| 162. #1999 | C2×C61 | semidirect |
| 163. #1875 | C2×C61 | semidirect |
| 164. #1780 | C2×C61 | semidirect |
| 172. C23×D4 | C22×C61 | semidirect |
| 178. C2×#121 | C22×C61 | semidirect |
| 181. C2×#117 | C22×C61 | semidirect |
| 183. C2×#102 | C22×C61 | semidirect |
| 184. C2×C22⋊C8 | C22×C61 | semidirect |
| 185. C2×C22⋊C8 | C22×C61 | semidirect |
| 186. #340 | C22×C61 | semidirect |
| 187. C61 | #23925 | direct (N × H) |
| 211. #121 | D4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C61×#535 | 2 |
| C2×C61×#447 | 2 |
| C61×#1999 | 2 |
| C61×#1875 | 2 |
| C61×#1780 | 2 |
| #23925 | 61 |