Finite Group DatabasebetaFinite Group DatabasebetaOrder 33536.
1044 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 1044 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×C131 | #392 |
| commutator, Frattini, cosocle | C23×C4 | C23×C131 |
| prime radical | #2433×C131 | C2 |
| LCS | G ▷ C23×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C131 ◁ C23×C4×C131 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #3193×C131 | C2 | semidirect |
| 2. #2435×C131 | C2 | semidirect |
| 4. #1783×C131 | C2 | semidirect |
| 5. #1508×C131 | C2 | semidirect |
| 6. #1507×C131 | C2 | semidirect |
| 7. #1297×C131 | C2 | semidirect |
| 32. C22×Q8×C131 | D4 | semidirect |
| 46. C2×M16×C131 | D4 | semidirect |
| 60. C2×C4⋊C4×C131 | D4 | semidirect |
| 79. #95×C131 | D4 | semidirect |
| 247. #10329 | C131 | direct (N × H) |
| 248. C131 | #10329 | direct (N × H) |
| 249. #3193 | C2×C131 | semidirect |
| 250. #2435 | C2×C131 | semidirect |
| 252. #1783 | C2×C131 | semidirect |
| 253. #1508 | C2×C131 | semidirect |
| 254. #1507 | C2×C131 | semidirect |
| 255. #1297 | C2×C131 | semidirect |
| 280. C22×Q8 | D4×C131 | semidirect |
| 294. C2×M16 | D4×C131 | semidirect |
| 308. C2×C4⋊C4 | D4×C131 | semidirect |
| 327. #95 | D4×C131 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #3193×C131 | 2 |
| #2435×C131 | 2 |
| #2433×C131 | 2 |
| #1783×C131 | 2 |
| #1508×C131 | 2 |
| #1507×C131 | 2 |
| #1297×C131 | 2 |
| #10329 | 131 |