Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
712 conjugacy classes of subgroups; only the 154 normal subgroups are shown.
This group has 712 conjugacy classes of subgroups — too many to draw. Only its 154 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 | #120 |
| commutator, Frattini, cosocle | C2×C42 | C23×C13 |
| prime radical | C13×#2537 | C2 |
| LCS | G ▷ C2×C42 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C23×C13 ◁ C2×C42×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#476 | C2 | semidirect |
| 3. C13×#1956 | C2 | semidirect |
| 4. C2×C13×D4⋊C8 | C2 | semidirect |
| 5. C13×#1296 | C2 | semidirect |
| 28. C13×C4⋊Q8 | D4 | semidirect |
| 44. C13×C4⋊C8 | D4 | semidirect |
| 49. #10235 | C13 | direct (N × H) |
| 93. C2×#476 | C2×C13 | semidirect |
| 95. #1956 | C2×C13 | semidirect |
| 96. C2×D4⋊C8 | C2×C13 | semidirect |
| 97. #1296 | C2×C13 | semidirect |
| 180. C4⋊Q8 | D4×C13 | semidirect |
| 196. C4⋊C8 | D4×C13 | semidirect |
| 250. C13 | #10235 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#476 | 2 |
| C13×#2537 | 2 |
| C13×#1956 | 2 |
| C2×C13×D4⋊C8 | 2 |
| C13×#1296 | 2 |
| #10235 | 13 |