Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
508 conjugacy classes of subgroups; only the 117 normal subgroups are shown.
This group has 508 conjugacy classes of subgroups — too many to draw. Only its 117 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×C16×D13 | C2 | semidirect |
| 3. C2×#11718159 | C2 | semidirect |
| 4. #13114871 | C2 | semidirect |
| 5. #13112933 | C2 | semidirect |
| 6. #13112932 | C2 | semidirect |
| 7. C2×C13×#359 | C2 | semidirect |
| 54. C2×C13×C16 | D4 | semidirect |
| 66. C2×#6090 | D4 | semidirect |
| 123. C2×#359 | D13 | semidirect |
| 193. C2×D13 | #359 | semidirect |
| 232. C2×C16 | C22⋊D13 | semidirect |
| 299. C13 | #13063 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C16×D13 | 2 |
| #13124413 | 2 |
| C2×#11718159 | 2 |
| #13114871 | 2 |
| #13112933 | 2 |
| #13112932 | 2 |
| C2×C13×#359 | 2 |
| #13063 | 13 |