Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
510 conjugacy classes of subgroups; only the 312 normal subgroups are shown.
This group has 510 conjugacy classes of subgroups — too many to draw. Only its 312 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 |
|---|---|---|
| 5. #11763697 | C4 | direct (N × H) |
| 6. C4×#63216 | C4 | semidirect |
| 39. #63216 | C42 | semidirect |
| 60. C4×C17 | #346 | semidirect |
| 87. C17 | C4×#346 | semidirect |
| 120. C4 | #11763697 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11763697 | 2 |
| C2×C4×#63216 | 2 |
| C42×#3622 | 2 |
| C4×#346 | 17 |