Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
918 conjugacy classes of subgroups; only the 251 normal subgroups are shown.
This group has 918 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×#88068 | C2 | semidirect |
| 3. #13117093 | C2 | direct (N × H) |
| 4. C2×C4×#6090 | C2 | semidirect |
| 5. C2×C13×#494 | C2 | semidirect |
| 13. C13×#494 | C22 | semidirect |
| 16. C2×#88068 | C22 | semidirect |
| 20. C4×#6090 | C22 | semidirect |
| 45. C2×#6090 | D4 | semidirect |
| 76. #6090 | C2×D4 | semidirect |
| 78. C2×#494 | D13 | semidirect |
| 91. C2×C4×C13 | SD32 | semidirect |
| 114. #494 | C2×D13 | semidirect |
| 127. C4×C13 | C2×SD32 | semidirect |
| 156. C2×C13 | #2248 | semidirect |
| 189. C13 | C2×#2248 | semidirect |
| 203. C2×C4 | #88068 | semidirect |
| 220. C4 | C2×#88068 | semidirect |
| 224. C2 | #13117093 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#88068 | 2 |
| C2×#11718356 | 2 |
| #13117093 | 2 |
| C2×C4×#6090 | 2 |
| C2×C13×#494 | 2 |
| C2×#2248 | 13 |