Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
552 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 95 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. #13124552 | C2 | semidirect |
| 2. #13124480 | C2 | semidirect |
| 3. C2×#11718155 | C2 | semidirect |
| 4. #13116572 | C2 | semidirect |
| 5. #13116465 | C2 | semidirect |
| 6. #13112951 | C2 | semidirect |
| 7. C2×C13×#509 | C2 | semidirect |
| 38. C2×C13×Q16 | D4 | semidirect |
| 46. C2×C13×D8 | D4 | semidirect |
| 69. C13×M32 | D4 | semidirect |
| 75. #88059 | D4 | semidirect |
| 143. C2×#509 | D13 | semidirect |
| 247. C2×Q16 | C22⋊D13 | semidirect |
| 255. C2×D8 | C22⋊D13 | semidirect |
| 275. M32 | C22⋊D13 | semidirect |
| 353. C13 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13124552 | 2 |
| #13124480 | 2 |
| C2×#11718155 | 2 |
| #13116572 | 2 |
| #13116465 | 2 |
| #13112951 | 2 |
| C2×C13×#509 | 2 |
| #13310 | 13 |