Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
680 conjugacy classes of subgroups; only the 134 normal subgroups are shown.
This group has 680 conjugacy classes of subgroups — too many to draw. Only its 134 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 | C2×C13×#127 | C22 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C13 ◁ C22×C4×C13 ◁ C2×C4×D4×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C13×#1799 | C2 | semidirect |
| 4. C13×#1393 | C2 | semidirect |
| 7. C2×C4×D4×C13 | C4 | semidirect |
| 11. C13×#390 | C4 | semidirect |
| 13. C13×#384 | C4 | semidirect |
| 15. C43×C13 | C4 | semidirect |
| 48. #12797 | C13 | direct (N × H) |
| 60. C2×D4×C13 | C4⋊C4 | semidirect |
| 94. C42×C13 | C4⋊C4 | semidirect |
| 97. #1799 | C2×C13 | semidirect |
| 98. #1393 | C2×C13 | semidirect |
| 146. C2×C4×D4 | C4×C13 | semidirect |
| 150. #390 | C4×C13 | semidirect |
| 152. #384 | C4×C13 | semidirect |
| 154. C43 | C4×C13 | semidirect |
| 183. C4×C13 | #353 | semidirect |
| 233. C2×D4 | C13×C4⋊C4 | semidirect |
| 267. C42 | C13×C4⋊C4 | semidirect |
| 268. C13 | #12797 | direct (N × H) |
| 340. C4 | C13×#353 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×C13×#127 | 2 |
| C2×C13×#353 | 2 |
| C13×#1799 | 2 |
| C13×#1393 | 2 |
| #12797 | 13 |