Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
568 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 99 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. #13127970 | C2 | semidirect |
| 2. C2×#11718854 | C2 | semidirect |
| 3. #13125322 | C2 | semidirect |
| 4. #13116571 | C2 | semidirect |
| 5. #13116551 | C2 | semidirect |
| 6. #13112922 | C2 | semidirect |
| 7. C13×#1976 | C2 | semidirect |
| 40. C2×C13×Q16 | D4 | semidirect |
| 42. C2×C13×D8 | D4 | semidirect |
| 83. #88052 | D4 | semidirect |
| 85. C2×#6090 | D4 | semidirect |
| 153. #1976 | D13 | semidirect |
| 257. C2×Q16 | D52 | semidirect |
| 269. C2×D8 | D52 | semidirect |
| 364. C13 | #13334 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127970 | 2 |
| C2×#11718854 | 2 |
| #13125322 | 2 |
| #13116571 | 2 |
| #13116551 | 2 |
| #13112922 | 2 |
| C13×#1976 | 2 |
| #13334 | 13 |