Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
426 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 426 conjugacy classes of subgroups — too many to draw. Only its 70 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C61 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C61 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C61 ◁ C2×C4×C61 ◁ C2×M16×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3197 | C2 | semidirect |
| 2. C61×#2191 | C2 | semidirect |
| 3. C61×#2190 | C2 | semidirect |
| 4. C61×#2010 | C2 | semidirect |
| 5. C61×#1340 | C2 | semidirect |
| 6. C61×#1339 | C2 | semidirect |
| 7. C61×#1320 | C2 | semidirect |
| 34. C2×Q16×C61 | D4 | semidirect |
| 36. C2×D8×C61 | D4 | semidirect |
| 61. #106×C61 | D4 | semidirect |
| 62. #106×C61 | D4 | semidirect |
| 166. #12116 | C61 | direct (N × H) |
| 189. #3197 | C2×C61 | semidirect |
| 190. #2191 | C2×C61 | semidirect |
| 191. #2190 | C2×C61 | semidirect |
| 192. #2010 | C2×C61 | semidirect |
| 193. #1340 | C2×C61 | semidirect |
| 194. #1339 | C2×C61 | semidirect |
| 195. #1320 | C2×C61 | semidirect |
| 221. C61 | #12116 | direct (N × H) |
| 229. C2×Q16 | D4×C61 | semidirect |
| 231. C2×D8 | D4×C61 | semidirect |
| 256. #106 | D4×C61 | semidirect |
| 257. #106 | D4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3197 | 2 |
| C61×#2191 | 2 |
| C61×#2190 | 2 |
| C61×#2010 | 2 |
| C61×#1340 | 2 |
| C61×#1339 | 2 |
| C61×#1320 | 2 |
| #12116 | 61 |