Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
254 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 254 conjugacy classes of subgroups — too many to draw. Only its 74 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. #13130417 | C2 | semidirect |
| 2. D8×#1057 | C2 | semidirect |
| 3. #13129870 | C2 | semidirect |
| 4. #13129791 | C2 | semidirect |
| 5. #13129790 | C2 | semidirect |
| 6. #13129747 | C2 | semidirect |
| 39. #88066 | C8 | semidirect |
| 57. C13×D8 | C2×C8 | semidirect |
| 66. D104 | C2×C8 | semidirect |
| 69. #6090 | C2×C8 | semidirect |
| 162. D8 | D13⋊C8 | semidirect |
| 180. C13 | #12045 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13130417 | 2 |
| D8×#1057 | 2 |
| #13129870 | 2 |
| #13129791 | 2 |
| #13129790 | 2 |
| #13129747 | 2 |
| #13116680 | 2 |
| #12045 | 13 |