Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
698 conjugacy classes of subgroups; only the 146 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 146 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C13 | C2×D8 |
| commutator, Frattini, cosocle | C22×C8 | C23×C13 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ C2×C4×C8×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C13×D16 | C2 | semidirect |
| 2. C2×C13×#493 | C2 | semidirect |
| 3. C2×C13×#357 | C2 | semidirect |
| 4. C13×#1970 | C2 | semidirect |
| 5. C13×#1374 | C2 | semidirect |
| 35. C2×C13×D8 | D4 | semidirect |
| 46. C2×C13×C16 | D4 | semidirect |
| 50. #13325 | C13 | direct (N × H) |
| 91. C22×D16 | C2×C13 | semidirect |
| 92. C2×#493 | C2×C13 | semidirect |
| 93. C2×#357 | C2×C13 | semidirect |
| 94. #1970 | C2×C13 | semidirect |
| 95. #1374 | C2×C13 | semidirect |
| 120. C2×C4×C13 | D16 | semidirect |
| 180. C2×D8 | D4×C13 | semidirect |
| 191. C2×C16 | D4×C13 | semidirect |
| 242. C13 | #13325 | direct (N × H) |
| 267. C2×C4 | C13×D16 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×D16 | 2 |
| C2×C13×#493 | 2 |
| C2×C13×#357 | 2 |
| C13×#1970 | 2 |
| C13×#1374 | 2 |
| #13325 | 13 |