Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2818 conjugacy classes of subgroups; only the 374 normal subgroups are shown.
This group has 2818 conjugacy classes of subgroups — too many to draw. Only its 374 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C13 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C13 |
| prime radical | C26×C13 | C22 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C13 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#397 | C2 | semidirect |
| 3. C13×#1439 | C2 | semidirect |
| 4. C13×#1437 | C2 | semidirect |
| 5. C13×#1437 | C2 | semidirect |
| 7. C22×C13×C4⋊C4 | C22 | semidirect |
| 12. C22×C42×C13 | C22 | semidirect |
| 15. C2×C13×#95 | C22 | semidirect |
| 16. C2×C13×#95 | C22 | semidirect |
| 17. C2×C13×#95 | C22 | semidirect |
| 45. #15480 | C13 | direct (N × H) |
| 90. C2×#397 | C2×C13 | semidirect |
| 92. #1439 | C2×C13 | semidirect |
| 93. #1437 | C2×C13 | semidirect |
| 94. #1437 | C2×C13 | semidirect |
| 147. C22×C4⋊C4 | C22×C13 | semidirect |
| 152. C22×C42 | C22×C13 | semidirect |
| 155. C2×#95 | C22×C13 | semidirect |
| 156. C2×#95 | C22×C13 | semidirect |
| 157. C2×#95 | C22×C13 | semidirect |
| 259. C13 | #15480 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#397 | 2 |
| C2×C13×#379 | 2 |
| C13×#1439 | 2 |
| C13×#1437 | 2 |
| #15480 | 13 |