Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
512 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 512 conjugacy classes of subgroups — too many to draw. Only its 92 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. #14545439 | C2 | semidirect |
| 2. #14545093 | C2 | semidirect |
| 3. C2×#11763721 | C2 | semidirect |
| 4. #14545024 | C2 | semidirect |
| 5. #14543860 | C2 | semidirect |
| 6. #14543847 | C2 | semidirect |
| 25. #11763080 | C4 | semidirect |
| 26. #11763079 | C4 | semidirect |
| 29. #11763076 | C4 | semidirect |
| 32. C17×#472 | C4 | semidirect |
| 43. C2×D8×C17 | C2×C4 | semidirect |
| 63. C2×D136 | C2×C4 | semidirect |
| 81. C17×#108 | C2×C4 | semidirect |
| 87. #10587490 | C2×C4 | semidirect |
| 248. #472 | #595 | semidirect |
| 287. C2×D8 | C2×#595 | semidirect |
| 314. #108 | C2×#595 | semidirect |
| 326. C17 | #12996 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545439 | 2 |
| #14545093 | 2 |
| C2×#11763721 | 2 |
| #14545024 | 2 |
| #14543860 | 2 |
| #14543847 | 2 |
| D17×#472 | 2 |
| #12996 | 17 |