Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
1174 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1174 conjugacy classes of subgroups — too many to draw. Only its 106 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×#3192 | C2 | semidirect |
| 2. C61×#2433 | C2 | semidirect |
| 3. C61×#1783 | C2 | semidirect |
| 4. C61×#1507 | C2 | semidirect |
| 5. C61×#1297 | C2 | semidirect |
| 28. C22×D4×C61 | D4 | semidirect |
| 32. C2×M16×C61 | D4 | semidirect |
| 39. C2×C4⋊C4×C61 | D4 | semidirect |
| 49. #95×C61 | D4 | semidirect |
| 132. #10326 | C61 | direct (N × H) |
| 155. #3192 | C2×C61 | semidirect |
| 156. #2433 | C2×C61 | semidirect |
| 157. #1783 | C2×C61 | semidirect |
| 158. #1507 | C2×C61 | semidirect |
| 159. #1297 | C2×C61 | semidirect |
| 180. C61 | #10326 | direct (N × H) |
| 189. C22×D4 | D4×C61 | semidirect |
| 193. C2×M16 | D4×C61 | semidirect |
| 200. C2×C4⋊C4 | D4×C61 | semidirect |
| 210. #95 | D4×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3192 | 2 |
| C61×#2433 | 2 |
| C61×#1783 | 2 |
| C61×#1507 | 2 |
| C61×#1297 | 2 |
| #10326 | 61 |