Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
466 conjugacy classes of subgroups; only the 202 normal subgroups are shown.
This group has 466 conjugacy classes of subgroups — too many to draw. Only its 202 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C13 | C2×D16 |
| commutator, Frattini, cosocle | C16 | C24×C13 |
| socle | C2×C13 | C22×D16 |
| LCS | G ▷ C16 ▷ C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C13 ◁ C22×C4×C13 ◁ C22×C8×C13 ◁ C22×C13×C16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C13×#508 | C2 | semidirect |
| 2. C13×#2264 | C2 | semidirect |
| 3. C13×#2263 | C2 | semidirect |
| 4. C13×#2262 | C2 | semidirect |
| 5. C2×C13×M64 | C2 | semidirect |
| 10. C13×#508 | C22 | semidirect |
| 11. C2×C13×Q32 | C22 | semidirect |
| 13. C2×C13×D16 | C22 | semidirect |
| 15. C13×Q64 | C22 | semidirect |
| 16. C13×SD64 | C22 | semidirect |
| 17. C13×D32 | C22 | semidirect |
| 18. C13×M64 | C22 | semidirect |
| 19. C2×C13×C32 | C22 | semidirect |
| 40. #33981 | C13 | direct (N × H) |
| 63. C2×#508 | C2×C13 | semidirect |
| 64. #2264 | C2×C13 | semidirect |
| 65. #2263 | C2×C13 | semidirect |
| 66. #2262 | C2×C13 | semidirect |
| 67. C2×M64 | C2×C13 | semidirect |
| 90. #508 | C22×C13 | semidirect |
| 91. C2×Q32 | C22×C13 | semidirect |
| 93. C2×D16 | C22×C13 | semidirect |
| 95. Q64 | C22×C13 | semidirect |
| 96. SD64 | C22×C13 | semidirect |
| 97. D32 | C22×C13 | semidirect |
| 98. M64 | C22×C13 | semidirect |
| 99. C2×C32 | C22×C13 | semidirect |
| 155. C13 | #33981 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C13×#508 | 2 |
| C13×#2264 | 2 |
| C13×#2263 | 2 |
| C13×#2262 | 2 |
| C2×C13×M64 | 2 |
| #33981 | 13 |