Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
476 conjugacy classes of subgroups; only the 82 normal subgroups are shown.
This group has 476 conjugacy classes of subgroups — too many to draw. Only its 82 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. #14545547 | C2 | semidirect |
| 2. #14545104 | C2 | semidirect |
| 3. C2×#11763726 | C2 | semidirect |
| 4. #14544943 | C2 | semidirect |
| 5. #14543856 | C2 | semidirect |
| 6. #14543836 | C2 | semidirect |
| 25. #11763250 | C4 | semidirect |
| 26. #11763247 | C4 | semidirect |
| 28. #11763244 | C4 | semidirect |
| 32. C17×#510 | C4 | semidirect |
| 45. C2×Q16×C17 | C2×C4 | semidirect |
| 59. C2×D136 | C2×C4 | semidirect |
| 76. C17×M32 | C2×C4 | semidirect |
| 81. #10587483 | C2×C4 | semidirect |
| 222. #510 | #595 | semidirect |
| 262. C2×Q16 | C2×#595 | semidirect |
| 289. M32 | C2×#595 | semidirect |
| 302. C17 | #13030 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545547 | 2 |
| #14545104 | 2 |
| C2×#11763726 | 2 |
| #14544943 | 2 |
| #14543856 | 2 |
| #14543836 | 2 |
| #14541919 | 2 |
| #13030 | 17 |