Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
794 conjugacy classes of subgroups; only the 105 normal subgroups are shown.
This group has 794 conjugacy classes of subgroups — too many to draw. Only its 105 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. #13125751 | C2 | semidirect |
| 2. #13119782 | C2 | semidirect |
| 3. #13113505 | C2 | semidirect |
| 4. #13113331 | C2 | semidirect |
| 5. #13113227 | C2 | semidirect |
| 6. #13112737 | C2 | semidirect |
| 7. C13×#3036 | C2 | semidirect |
| 43. C13×C4⋊Q8 | D4 | semidirect |
| 44. C13×#127 | D4 | semidirect |
| 69. C13×C4⋊C8 | D4 | semidirect |
| 77. C4⋊#1055 | D4 | semidirect |
| 97. C2×D4×C13 | D8 | semidirect |
| 147. #3036 | D13 | semidirect |
| 276. C4⋊Q8 | C22⋊D13 | semidirect |
| 283. #127 | C22⋊D13 | semidirect |
| 303. C4⋊C8 | C22⋊D13 | semidirect |
| 351. C2×D4 | #6104 | semidirect |
| 385. C13 | #10238 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13125751 | 2 |
| #13119782 | 2 |
| #13113505 | 2 |
| #13113331 | 2 |
| #13113227 | 2 |
| #13112737 | 2 |
| C13×#3036 | 2 |
| #10238 | 13 |