Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
444 conjugacy classes of subgroups; only the 78 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 78 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 |
|---|---|---|
| 3. #14543757 | C2 | semidirect |
| 4. #14543756 | C2 | semidirect |
| 12. C2×Q16×D17 | C4 | semidirect |
| 16. #11763067 | C4 | semidirect |
| 20. #106×D17 | C4 | semidirect |
| 22. C17×#470 | C4 | semidirect |
| 32. C2×Q16×C17 | C2×C4 | semidirect |
| 43. C2×Dic68 | C2×C4 | semidirect |
| 57. C17×#106 | C2×C4 | semidirect |
| 60. #10587488 | C2×C4 | semidirect |
| 198. #470 | #595 | semidirect |
| 210. D17 | #1340 | semidirect |
| 217. C2×Q16 | C2×#595 | semidirect |
| 247. #106 | C2×#595 | semidirect |
| 252. C17 | C2×#1340 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545018 | 2 |
| #14544456 | 2 |
| #14543757 | 2 |
| #14543756 | 2 |
| D17×#470 | 2 |
| C2×#1340 | 17 |