Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
572 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 90 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 | B(4,𝔽2) |
| commutator, Frattini, cosocle | C22×Q8 | C23×C13 |
| prime radical | C2×C13×2−1+4 | C22 |
| LCS | G ▷ C22×Q8 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C23×C13 ◁ C22×Q8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C13×#2811 | C2 | semidirect |
| 3. C13×#1394 | C2 | semidirect |
| 13. C13×2−1+4 | Q8 | semidirect |
| 30. #13378 | C13 | direct (N × H) |
| 61. #2811 | C2×C13 | semidirect |
| 63. #1394 | C2×C13 | semidirect |
| 111. 2−1+4 | Q8×C13 | semidirect |
| 164. C13 | #13378 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C13×#2811 | 2 |
| C13×#1793 | 2 |
| C13×#1394 | 2 |
| #13378 | 13 |