Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1422 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 1422 conjugacy classes of subgroups — too many to draw. Only its 312 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C23×#261 |
| commutator, socle | C23×C13 | C23×C4 |
| Fitting | C13×#383 | C4 |
| prime radical, cosocle | C23×D13 | C24 |
| hypercenter | #383 | #261 |
| hypocenter | C13 | #14710 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #383 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 12. C13×#383 | C4 | semidirect |
| 13. #11718598 | C4 | semidirect |
| 15. #11718312 | C4 | semidirect |
| 51. C42×C13 | C4⋊C4 | semidirect |
| 52. C4×Dic13 | C4⋊C4 | semidirect |
| 83. #383 | #261 | semidirect |
| 139. C42 | C4⋊#261 | semidirect |
| 140. C13 | #14710 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719061 | 2 |
| C2×C42×#261 | 2 |
| #13130016 | 2 |
| D13×#383 | 2 |
| #14710 | 13 |