Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
724 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 724 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 |
|---|---|---|
| 1. C4×D4×#595 | C2 | semidirect |
| 2. #14544917 | C2 | semidirect |
| 3. #14544165 | C2 | semidirect |
| 4. #14544110 | C2 | semidirect |
| 5. #14543681 | C2 | semidirect |
| 6. #14543611 | C2 | semidirect |
| 25. #11763086 | C4 | semidirect |
| 26. #11763005 | C4 | semidirect |
| 27. #11763004 | C4 | semidirect |
| 32. C17×#474 | C4 | semidirect |
| 50. C17×C4⋊Q8 | C2×C4 | semidirect |
| 65. #10587560 | C2×C4 | semidirect |
| 78. C17×C4⋊C8 | C2×C4 | semidirect |
| 86. C4⋊#3622 | C2×C4 | semidirect |
| 135. C4×#595 | D8 | semidirect |
| 179. D4×C17 | #104 | semidirect |
| 202. D68 | #104 | semidirect |
| 266. #474 | #595 | semidirect |
| 300. C4⋊Q8 | C2×#595 | semidirect |
| 334. C4⋊C8 | C2×#595 | semidirect |
| 347. C17 | #9233 | semidirect |
| 439. D4 | #10587550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4×D4×#595 | 2 |
| #14544917 | 2 |
| #14544165 | 2 |
| #14544110 | 2 |
| #14543681 | 2 |
| #14543611 | 2 |
| #14538786 | 2 |
| #9233 | 17 |