Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
134 conjugacy classes of subgroups; only the 47 normal subgroups are shown.
This group has 134 conjugacy classes of subgroups — too many to draw. Only its 47 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2 | C2×D416 |
| commutator, cosocle | C13×C32 | C23 |
| Frattini | C32 | C22×D13 |
| Fitting | C13×M128 | C2 |
| socle | C2×C13 | C2×D32 |
| hypercenter | M128 | D13 |
| hypocenter | C13 | #13742 |
| LCS | G ▷ C13×C32 ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13 | |
| UCS | C1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ C2×C32 ◁ M128 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #13117145 | C2 | semidirect |
| 2. C2×D416 | C2 | semidirect |
| 3. #13113052 | C2 | semidirect |
| 4. D832 | C2 | semidirect |
| 5. C13×M128 | C2 | semidirect |
| 9. Dic208 | C22 | semidirect |
| 13. D416 | C22 | semidirect |
| 14. C13×C64 | C22 | semidirect |
| 40. M128 | D13 | semidirect |
| 59. C64 | C2×D13 | semidirect |
| 91. C13 | #13742 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13117145 | 2 |
| C2×D416 | 2 |
| #13113052 | 2 |
| D832 | 2 |
| C13×M128 | 2 |
| #13742 | 13 |