Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
654 conjugacy classes of subgroups; only the 360 normal subgroups are shown.
This group has 654 conjugacy classes of subgroups — too many to draw. Only its 360 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 |
|---|---|---|
| 6. #11763650 | C4 | direct (N × H) |
| 21. C4×C8×C17 | C8 | semidirect |
| 22. C8×Dic17 | C8 | semidirect |
| 24. C4×#3622 | C8 | semidirect |
| 55. C8×C17 | C4×C8 | semidirect |
| 56. #3622 | C4×C8 | semidirect |
| 64. C4×C17 | #322 | semidirect |
| 67. Dic17 | #322 | semidirect |
| 93. C4×C8 | #3624 | semidirect |
| 94. C17 | C4×#322 | semidirect |
| 125. C8 | C4×#3624 | semidirect |
| 132. C4 | #11763650 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C42×#3624 | 2 |
| C2×#11763650 | 2 |
| C4×C8×Dic17 | 2 |
| C4×#322 | 17 |