Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
572 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 100 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. C22×#88101 | C2 | semidirect |
| 2. C2×#11718279 | C2 | semidirect |
| 3. #13131064 | C2 | semidirect |
| 4. #13129907 | C2 | semidirect |
| 14. C13×#467 | C4 | semidirect |
| 15. #11718849 | C4 | semidirect |
| 16. #11718776 | C4 | semidirect |
| 18. #11718544 | C4 | semidirect |
| 32. C2×C13×Q16 | C2×C4 | semidirect |
| 41. C2×D104 | C2×C4 | semidirect |
| 57. #88101 | D4 | semidirect |
| 60. C13×#107 | C2×C4 | semidirect |
| 64. #88058 | C2×C4 | semidirect |
| 180. #467 | #261 | semidirect |
| 195. C22×C13 | #360 | semidirect |
| 206. C2×D13 | #360 | semidirect |
| 224. C2×Q16 | C2×#261 | semidirect |
| 252. #107 | C2×#261 | semidirect |
| 323. C13 | #13001 | semidirect |
| 385. C22 | #11718279 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88101 | 2 |
| C2×#11718279 | 2 |
| #13131064 | 2 |
| #13129907 | 2 |
| #13124419 | 2 |
| #13001 | 13 |