Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
552 conjugacy classes of subgroups; only the 99 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 99 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. #13127970 | C2 | semidirect |
| 2. #13125282 | C2 | semidirect |
| 3. #13116563 | C2 | semidirect |
| 4. #13112916 | C2 | semidirect |
| 5. C13×#1975 | C2 | semidirect |
| 27. C2×C13×Q16 | D4 | semidirect |
| 29. C2×C13×D8 | D4 | semidirect |
| 61. C2×#6090 | D4 | semidirect |
| 112. #1975 | D13 | semidirect |
| 192. C2×Q16 | D52 | semidirect |
| 198. C2×D8 | D52 | semidirect |
| 271. C13 | #13340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13127970 | 2 |
| #13125282 | 2 |
| #13116563 | 2 |
| #13112916 | 2 |
| C13×#1975 | 2 |
| #13340 | 13 |