Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
724 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 724 conjugacy classes of subgroups — too many to draw. Only its 96 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4×D4×#261 | C2 | semidirect |
| 2. #13130970 | C2 | semidirect |
| 3. #13130216 | C2 | semidirect |
| 4. #13130162 | C2 | semidirect |
| 5. #13129733 | C2 | semidirect |
| 6. #13129663 | C2 | semidirect |
| 21. C13×#459 | C4 | semidirect |
| 24. #11718733 | C4 | semidirect |
| 25. #11718668 | C4 | semidirect |
| 26. #11718507 | C4 | semidirect |
| 51. C13×#127 | C2×C4 | semidirect |
| 67. #88123 | C2×C4 | semidirect |
| 77. C13×C4⋊C8 | C2×C4 | semidirect |
| 86. C4⋊#1055 | C2×C4 | semidirect |
| 136. C4×#261 | D8 | semidirect |
| 189. D4×C13 | #104 | semidirect |
| 209. D52 | #104 | semidirect |
| 237. #459 | #261 | semidirect |
| 293. #127 | C2×#261 | semidirect |
| 326. C4⋊C8 | C2×#261 | semidirect |
| 417. C13 | #9233 | semidirect |
| 439. D4 | #88116 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×#261 | 2 |
| #13130970 | 2 |
| #13130216 | 2 |
| #13130162 | 2 |
| #13129733 | 2 |
| #13129663 | 2 |
| #13124835 | 2 |
| #9233 | 13 |