Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
1022 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 1022 conjugacy classes of subgroups — too many to draw. Only its 251 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. C22×#88066 | C2 | semidirect |
| 2. C2×#11718356 | C2 | semidirect |
| 3. #13117085 | C2 | direct (N × H) |
| 4. C2×C4×#6090 | C2 | semidirect |
| 5. C2×C13×#493 | C2 | semidirect |
| 13. C13×#493 | C22 | semidirect |
| 16. C2×#88066 | C22 | semidirect |
| 19. #11718356 | C22 | semidirect |
| 20. C4×#6090 | C22 | semidirect |
| 45. C2×#6090 | D4 | semidirect |
| 77. #6090 | C2×D4 | semidirect |
| 80. C2×#493 | D13 | semidirect |
| 94. C2×C4×C13 | D16 | semidirect |
| 119. #493 | C2×D13 | semidirect |
| 132. C4×C13 | C2×D16 | semidirect |
| 162. C2×C13 | #2246 | semidirect |
| 196. C13 | C2×#2246 | semidirect |
| 212. C2×C4 | #88066 | semidirect |
| 231. C4 | C2×#88066 | semidirect |
| 236. C2 | #13117085 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88066 | 2 |
| C2×#11718356 | 2 |
| #13117085 | 2 |
| C2×C4×#6090 | 2 |
| C2×C13×#493 | 2 |
| C2×#2246 | 13 |