Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 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 | C24×D13 |
| commutator, socle, cosocle | C23×C13 | C25 |
| Fitting | C13×#2868 | C2 |
| hypercenter | #2868 | D13 |
| hypocenter | C13 | #36644 |
| LCS | G ▷ C23×C13 ▷ C13 | |
| UCS | C1 ◁ C23 ◁ #2868 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#11719430 | C2 | semidirect |
| 2. #13123231 | C2 | semidirect |
| 3. #13123194 | C2 | semidirect |
| 4. #13123182 | C2 | semidirect |
| 5. #13117398 | C2 | semidirect |
| 6. C43×D13 | C2 | semidirect |
| 7. C13×#2868 | C2 | semidirect |
| 45. C42×D13 | D4 | semidirect |
| 66. C42×C13 | #41 | semidirect |
| 72. #2868 | D13 | semidirect |
| 96. C4×D13 | #127 | semidirect |
| 120. C4×C13 | #532 | semidirect |
| 173. C42 | #6131 | semidirect |
| 174. C13 | #36644 | semidirect |
| 204. C4 | #11719430 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11719430 | 2 |
| #13123231 | 2 |
| #13123194 | 2 |
| #13123182 | 2 |
| #13117398 | 2 |
| C43×D13 | 2 |
| C13×#2868 | 2 |
| #36644 | 13 |