Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
686 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 686 conjugacy classes of subgroups — too many to draw. Only its 96 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. #14544969 | C2 | semidirect |
| 3. #14544167 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11763100 | C4 | semidirect |
| 26. #11763099 | C4 | semidirect |
| 27. #11763011 | C4 | semidirect |
| 32. C17×#461 | C4 | semidirect |
| 50. C17×C4⋊Q8 | C2×C4 | semidirect |
| 67. #10587555 | C2×C4 | semidirect |
| 75. C17×C4⋊C8 | C2×C4 | semidirect |
| 84. C4⋊#3622 | C2×C4 | semidirect |
| 125. C4×#595 | SD16 | semidirect |
| 252. #461 | #595 | semidirect |
| 283. C4⋊Q8 | C2×#595 | semidirect |
| 317. C4⋊C8 | C2×#595 | semidirect |
| 328. C17 | #9231 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×#595 | 2 |
| #14544969 | 2 |
| #14544167 | 2 |
| #14544110 | 2 |
| #14543681 | 2 |
| #14543611 | 2 |
| #14538791 | 2 |
| #9231 | 17 |