Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
448 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 448 conjugacy classes of subgroups — too many to draw. Only its 76 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 |
|---|---|---|
| 1. #14545018 | C2 | semidirect |
| 2. #14544456 | C2 | semidirect |
| 3. #14543756 | C2 | semidirect |
| 4. #14543755 | C2 | semidirect |
| 12. C2×#10587605 | C4 | semidirect |
| 17. #11763062 | C4 | semidirect |
| 20. #11762844 | C4 | semidirect |
| 22. C17×#470 | C4 | semidirect |
| 32. C2×Q16×C17 | C2×C4 | semidirect |
| 43. C2×D136 | C2×C4 | semidirect |
| 57. C17×#106 | C2×C4 | semidirect |
| 61. #10587488 | C2×C4 | semidirect |
| 197. #470 | #595 | semidirect |
| 219. C2×Q16 | C2×#595 | semidirect |
| 251. #106 | C2×#595 | semidirect |
| 256. C17 | #11685 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545018 | 2 |
| #14544456 | 2 |
| #14543756 | 2 |
| #14543755 | 2 |
| #14538395 | 2 |
| #11685 | 17 |