Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
626 conjugacy classes of subgroups; only the 112 normal subgroups are shown.
This group has 626 conjugacy classes of subgroups — too many to draw. Only its 112 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. C22×#10587534 | C2 | semidirect |
| 2. C2×#11763721 | C2 | semidirect |
| 3. #14545009 | C2 | semidirect |
| 4. #14543841 | C2 | semidirect |
| 17. #11763046 | C4 | semidirect |
| 18. #11763045 | C4 | semidirect |
| 21. #11763042 | C4 | semidirect |
| 24. C17×#466 | C4 | semidirect |
| 33. C2×D8×C17 | C2×C4 | semidirect |
| 43. C2×D136 | C2×C4 | semidirect |
| 57. #10587534 | D4 | semidirect |
| 60. C17×#107 | C2×C4 | semidirect |
| 64. #10587489 | C2×C4 | semidirect |
| 191. C22×C17 | #357 | semidirect |
| 206. C2×D17 | #357 | semidirect |
| 232. #466 | #595 | semidirect |
| 260. C2×D8 | C2×#595 | semidirect |
| 289. #107 | C2×#595 | semidirect |
| 294. C17 | #12991 | semidirect |
| 433. C22 | #11763721 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587534 | 2 |
| C2×#11763721 | 2 |
| #14545009 | 2 |
| #14543841 | 2 |
| D17×#466 | 2 |
| #12991 | 17 |