Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
400 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 400 conjugacy classes of subgroups — too many to draw. Only its 92 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 |
|---|---|---|
| 2. #13131188 | C2 | semidirect |
| 3. C2×#11718222 | C2 | semidirect |
| 5. #13129911 | C2 | semidirect |
| 6. #13129898 | C2 | semidirect |
| 25. C13×#350 | C4 | semidirect |
| 26. #11718153 | C4 | semidirect |
| 27. #11718107 | C4 | semidirect |
| 28. #11718100 | C4 | semidirect |
| 62. C13×M32 | C2×C4 | semidirect |
| 63. C2×C13×C16 | C2×C4 | semidirect |
| 64. #88052 | C2×C4 | semidirect |
| 65. C2×#6090 | C2×C4 | semidirect |
| 184. #350 | #261 | semidirect |
| 227. M32 | C2×#261 | semidirect |
| 232. C2×C16 | C2×#261 | semidirect |
| 303. C13 | #12926 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #13131491 | 2 |
| #13131188 | 2 |
| C2×#11718222 | 2 |
| #13130725 | 2 |
| #13129911 | 2 |
| #13129898 | 2 |
| D13×#350 | 2 |
| #12926 | 13 |