Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
396 conjugacy classes of subgroups; only the 94 normal subgroups are shown.
This group has 396 conjugacy classes of subgroups — too many to draw. Only its 94 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×C131 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C131 |
| prime radical | C22×D4×C131 | D4 |
| LCS | G ▷ C2×C42 ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C131 ◁ C2×C42×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #2084×C131 | C2 | semidirect |
| 4. #2072×C131 | C2 | semidirect |
| 5. #1272×C131 | C2 | semidirect |
| 6. #1271×C131 | C2 | semidirect |
| 187. #7820 | C131 | direct (N × H) |
| 188. C131 | #7820 | direct (N × H) |
| 191. #2084 | C2×C131 | semidirect |
| 192. #2072 | C2×C131 | semidirect |
| 193. #1272 | C2×C131 | semidirect |
| 194. #1271 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #2808×C131 | 2 |
| #2093×C131 | 2 |
| #2084×C131 | 2 |
| #2072×C131 | 2 |
| #1272×C131 | 2 |
| #1271×C131 | 2 |
| #1270×C131 | 2 |
| #7820 | 131 |