Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1762 conjugacy classes of subgroups; only the 299 normal subgroups are shown.
This group has 1762 conjugacy classes of subgroups — too many to draw. Only its 299 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. C2×#11718815 | C2 | semidirect |
| 2. C2×#11718734 | C2 | semidirect |
| 3. C2×#11718354 | C2 | semidirect |
| 4. C2×#11718737 | C2 | semidirect |
| 5. #13123230 | C2 | semidirect |
| 6. #13123192 | C2 | semidirect |
| 7. C4×#88055 | C2 | semidirect |
| 8. C2×C13×#493 | C2 | semidirect |
| 64. C4×C8×C13 | D4 | semidirect |
| 65. #88055 | D4 | semidirect |
| 66. C4×#1055 | D4 | semidirect |
| 111. C2×#493 | D13 | semidirect |
| 148. C8×C13 | #127 | semidirect |
| 149. #1055 | #127 | semidirect |
| 183. C4×C13 | #496 | semidirect |
| 224. C4×C8 | C22⋊D13 | semidirect |
| 272. C13 | #33304 | semidirect |
| 305. C8 | #88194 | semidirect |
| 320. C4 | #11718815 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11718815 | 2 |
| C2×#11718734 | 2 |
| C2×#11718354 | 2 |
| C2×#11718737 | 2 |
| #13123230 | 2 |
| #13123192 | 2 |
| C4×#88055 | 2 |
| C2×C13×#493 | 2 |
| #33304 | 13 |