Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
572 conjugacy classes of subgroups; only the 100 normal subgroups are shown.
This group has 572 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 |
|---|---|---|
| 1. C22×#10587533 | C2 | semidirect |
| 2. C2×#11763726 | C2 | semidirect |
| 3. #14545012 | C2 | semidirect |
| 4. #14543855 | C2 | semidirect |
| 17. #11763047 | C4 | semidirect |
| 18. #11763046 | C4 | semidirect |
| 19. #11763045 | C4 | semidirect |
| 24. C17×#467 | C4 | semidirect |
| 32. C2×Q16×C17 | C2×C4 | semidirect |
| 41. C2×D136 | C2×C4 | semidirect |
| 57. #10587533 | D4 | semidirect |
| 60. C17×#107 | C2×C4 | semidirect |
| 64. #10587489 | C2×C4 | semidirect |
| 176. C22×C17 | #360 | semidirect |
| 187. C2×D17 | #360 | semidirect |
| 206. #467 | #595 | semidirect |
| 232. C2×Q16 | C2×#595 | semidirect |
| 260. #107 | C2×#595 | semidirect |
| 269. C17 | #13001 | semidirect |
| 385. C22 | #11763726 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#10587533 | 2 |
| C2×#11763726 | 2 |
| #14545012 | 2 |
| #14543855 | 2 |
| #14538367 | 2 |
| #13001 | 17 |