Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
538 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 538 conjugacy classes of subgroups — too many to draw. Only its 100 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. #14544086 | C2 | semidirect |
| 4. #14543608 | C2 | semidirect |
| 56. C2×Q8×C17 | M16 | semidirect |
| 77. C42×C17 | M16 | semidirect |
| 203. C17 | #9103 | semidirect |
| 208. C2×Q8 | #63247 | semidirect |
| 240. C42 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545646 | 2 |
| #14544086 | 2 |
| #14544024 | 2 |
| #14543608 | 2 |
| #14531497 | 2 |
| #9103 | 17 |