Finite Group DatabasebetaFinite Group DatabasebetaOrder 15616.
434 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 434 conjugacy classes of subgroups — too many to draw. Only its 82 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 | #447 |
| commutator, Frattini, cosocle | C22×C8 | C23×C61 |
| LCS | G ▷ C22×C8 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C61 ◁ C22×C4×C61 ◁ C2×C4⋊C8×C61 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C61×#3245 | C2 | semidirect |
| 2. C61×#2184 | C2 | semidirect |
| 3. C61×#2054 | C2 | semidirect |
| 4. C61×#1347 | C2 | semidirect |
| 5. C61×#1322 | C2 | semidirect |
| 115. C2×C4×C61 | D16 | semidirect |
| 120. #12158 | C61 | direct (N × H) |
| 143. #3245 | C2×C61 | semidirect |
| 144. #2184 | C2×C61 | semidirect |
| 145. #2054 | C2×C61 | semidirect |
| 146. #1347 | C2×C61 | semidirect |
| 147. #1322 | C2×C61 | semidirect |
| 168. C61 | #12158 | direct (N × H) |
| 265. C2×C4 | D16×C61 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C61×#3245 | 2 |
| C61×#2184 | 2 |
| C61×#2054 | 2 |
| C61×#1347 | 2 |
| C61×#1322 | 2 |
| #12158 | 61 |