Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 90 normal subgroups are shown.
This group has 492 conjugacy classes of subgroups — too many to draw. Only its 90 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. #14545438 | C2 | semidirect |
| 2. #14545106 | C2 | semidirect |
| 3. C2×#11763726 | C2 | semidirect |
| 4. #14545027 | C2 | semidirect |
| 5. #14543864 | C2 | semidirect |
| 6. #14543850 | C2 | semidirect |
| 25. #11763081 | C4 | semidirect |
| 26. #11763080 | C4 | semidirect |
| 27. #11763079 | C4 | semidirect |
| 32. C17×#473 | C4 | semidirect |
| 43. C2×Q16×C17 | C2×C4 | semidirect |
| 63. C2×D136 | C2×C4 | semidirect |
| 81. C17×#108 | C2×C4 | semidirect |
| 87. #10587490 | C2×C4 | semidirect |
| 236. #473 | #595 | semidirect |
| 275. C2×Q16 | C2×#595 | semidirect |
| 304. #108 | C2×#595 | semidirect |
| 316. C17 | #13005 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545438 | 2 |
| #14545106 | 2 |
| C2×#11763726 | 2 |
| #14545027 | 2 |
| #14543864 | 2 |
| #14543850 | 2 |
| #14538506 | 2 |
| #13005 | 17 |