Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
404 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 404 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×C131 | #1595 |
| commutator, Frattini, cosocle | C2×M16 | C23×C131 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C131 ◁ C2×C4×C131 ◁ C2×M16×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3204×C131 | C2 | semidirect |
| 2. #2191×C131 | C2 | semidirect |
| 3. #2190×C131 | C2 | semidirect |
| 4. #2017×C131 | C2 | semidirect |
| 5. #1342×C131 | C2 | semidirect |
| 6. #1341×C131 | C2 | semidirect |
| 7. #1321×C131 | C2 | semidirect |
| 190. #12119 | C131 | direct (N × H) |
| 191. C131 | #12119 | direct (N × H) |
| 192. #3204 | C2×C131 | semidirect |
| 193. #2191 | C2×C131 | semidirect |
| 194. #2190 | C2×C131 | semidirect |
| 195. #2017 | C2×C131 | semidirect |
| 196. #1342 | C2×C131 | semidirect |
| 197. #1341 | C2×C131 | semidirect |
| 198. #1321 | C2×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3204×C131 | 2 |
| #2191×C131 | 2 |
| #2190×C131 | 2 |
| #2017×C131 | 2 |
| #1342×C131 | 2 |
| #1341×C131 | 2 |
| #1321×C131 | 2 |
| #12119 | 131 |