Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
884 conjugacy classes of subgroups; only the 206 normal subgroups are shown.
This group has 884 conjugacy classes of subgroups — too many to draw. Only its 206 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 ◁ C61×#376 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#2657 | C2 | semidirect |
| 2. C61×#2644 | C2 | semidirect |
| 3. C61×#2042 | C2 | semidirect |
| 4. C61×#2041 | C2 | semidirect |
| 5. C61×#2012 | C2 | semidirect |
| 6. C61×#2011 | C2 | semidirect |
| 7. C61×#1840 | C2 | semidirect |
| 127. #32802 | C61 | direct (N × H) |
| 147. #2657 | C2×C61 | semidirect |
| 148. #2644 | C2×C61 | semidirect |
| 149. #2042 | C2×C61 | semidirect |
| 150. #2041 | C2×C61 | semidirect |
| 151. #2012 | C2×C61 | semidirect |
| 152. #2011 | C2×C61 | semidirect |
| 153. #1840 | C2×C61 | semidirect |
| 176. C61 | #32802 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#2657 | 2 |
| C61×#2644 | 2 |
| C61×#2042 | 2 |
| C61×#2041 | 2 |
| C61×#2012 | 2 |
| C61×#2011 | 2 |
| C61×#1840 | 2 |
| #32802 | 61 |