Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
504 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 504 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. #14544027 | C2 | semidirect |
| 5. #14543624 | C2 | semidirect |
| 6. #14543610 | C2 | semidirect |
| 74. C2×Q8×C17 | M16 | semidirect |
| 98. C2×C8×C17 | M16 | semidirect |
| 252. C17 | #9091 | semidirect |
| 259. C2×Q8 | #63247 | semidirect |
| 286. C2×C8 | #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 |
| #14544083 | 2 |
| #14544027 | 2 |
| #14543624 | 2 |
| #14543610 | 2 |
| C2×#11762910 | 2 |
| #9091 | 17 |