Finite Group DatabasebetaFinite Group DatabasebetaOrder 3328.
4126 conjugacy classes of subgroups; only the 2232 normal subgroups are shown.
This group has 4126 conjugacy classes of subgroups — too many to draw. Only its 2232 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. C22×#88110 | C2 | direct (N × H) |
| 7. C23×#1057 | C4 | semidirect |
| 11. C2×#88110 | C22 | direct (N × H) |
| 20. C22×#1057 | C2×C4 | semidirect |
| 24. #88110 | C23 | direct (N × H) |
| 38. C2×#1057 | C22×C4 | semidirect |
| 45. C23×C13 | #97 | semidirect |
| 58. #1057 | C23×C4 | semidirect |
| 67. C22×C13 | C2×#97 | semidirect |
| 89. C2×C13 | C22×#97 | semidirect |
| 109. C13 | C23×#97 | semidirect |
| 110. C23 | #88110 | direct (N × H) |
| 124. C22 | C2×#88110 | direct (N × H) |
| 133. C2 | C22×#88110 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C24×#1057 | 2 |
| C22×#88110 | 2 |
| C23×C4×Dic13 | 2 |
| C23×#97 | 13 |