Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
2502 conjugacy classes of subgroups; only the 667 normal subgroups are shown.
This group has 2502 conjugacy classes of subgroups — too many to draw. Only its 667 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×#88130 | C2 | semidirect |
| 2. #13122910 | C2 | direct (N × H) |
| 3. C2×#11718644 | C2 | semidirect |
| 4. C2×#11718655 | C2 | semidirect |
| 6. C2×C13×#384 | C2 | semidirect |
| 16. C2×#88130 | C22 | semidirect |
| 17. C13×#384 | C22 | semidirect |
| 20. #11718655 | C22 | semidirect |
| 22. #11718644 | C22 | semidirect |
| 34. C2×C42×C13 | D4 | semidirect |
| 70. C42×C13 | C2×D4 | semidirect |
| 80. C2×#384 | D13 | semidirect |
| 118. #384 | C2×D13 | semidirect |
| 155. C2×C42 | D52 | semidirect |
| 159. C2×C13 | #2823 | semidirect |
| 190. C42 | C2×D52 | semidirect |
| 191. C13 | C2×#2823 | semidirect |
| 231. C2 | #13122910 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88130 | 2 |
| #13122910 | 2 |
| C2×#11718644 | 2 |
| C2×#11718655 | 2 |
| C2×#11718652 | 2 |
| C2×C13×#384 | 2 |
| C2×#2823 | 13 |