Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1206 conjugacy classes of subgroups; only the 158 normal subgroups are shown.
This group has 1206 conjugacy classes of subgroups — too many to draw. Only its 158 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 | C22×C4 | C22×C4×C13 |
| Frattini, cosocle | C22×D4 | C23×C13 |
| prime radical | C23×D4×C13 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C24×C13 ◁ C23×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×C13×#354 | C2 | semidirect |
| 4. C23×Q8×C13 | C4 | semidirect |
| 8. C2×C13×#124 | C4 | semidirect |
| 11. C22×C42×C13 | C4 | semidirect |
| 46. #12694 | C13 | direct (N × H) |
| 61. C2×Q8×C13 | C22⋊C4 | semidirect |
| 92. C42×C13 | C22⋊C4 | semidirect |
| 94. C2×#354 | C2×C13 | semidirect |
| 136. C23×Q8 | C4×C13 | semidirect |
| 140. C2×#124 | C4×C13 | semidirect |
| 143. C22×C42 | C4×C13 | semidirect |
| 162. C22×C13 | #354 | semidirect |
| 222. C2×Q8 | C13×C22⋊C4 | semidirect |
| 253. C42 | C13×C22⋊C4 | semidirect |
| 254. C13 | #12694 | direct (N × H) |
| 309. C22 | C13×#354 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C13×#124 | 2 |
| C2×C13×#354 | 2 |
| C13×#1781 | 2 |
| #12694 | 13 |