Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
616 conjugacy classes of subgroups; only the 126 normal subgroups are shown.
This group has 616 conjugacy classes of subgroups — too many to draw. Only its 126 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×C13 | C2×#99 |
| commutator | C24 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C22×D4×C13 | C23 |
| LCS | G ▷ C24 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C23×Q8×C13 | C4 | semidirect |
| 15. C13×#385 | C4 | semidirect |
| 16. C13×#380 | C4 | semidirect |
| 47. C13×#99 | Q8 | semidirect |
| 52. #13296 | C13 | direct (N × H) |
| 148. C23×Q8 | C4×C13 | semidirect |
| 158. #385 | C4×C13 | semidirect |
| 159. #380 | C4×C13 | semidirect |
| 215. #99 | Q8×C13 | semidirect |
| 273. C13 | #13296 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2409 | 2 |
| C13×#1800 | 2 |
| C4×C13×#99 | 2 |
| C13×#1390 | 2 |
| #13296 | 13 |