Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
492 conjugacy classes of subgroups; only the 92 normal subgroups are shown.
This group has 492 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 |
|---|---|---|
| 2. #14545094 | C2 | semidirect |
| 3. C2×#11763722 | C2 | semidirect |
| 5. #14543860 | C2 | semidirect |
| 6. #14543847 | C2 | semidirect |
| 25. #11763085 | C4 | semidirect |
| 26. #11763084 | C4 | semidirect |
| 29. #11763081 | C4 | semidirect |
| 32. C17×#473 | C4 | semidirect |
| 43. C2×Q16×C17 | C2×C4 | semidirect |
| 63. C2×Dic68 | C2×C4 | semidirect |
| 81. C17×#108 | C2×C4 | semidirect |
| 87. #10587490 | C2×C4 | semidirect |
| 241. #473 | #595 | semidirect |
| 277. C2×Q16 | C2×#595 | semidirect |
| 305. #108 | C2×#595 | semidirect |
| 317. C17 | #12997 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545439 | 2 |
| #14545094 | 2 |
| C2×#11763722 | 2 |
| #14545024 | 2 |
| #14543860 | 2 |
| #14543847 | 2 |
| D17×#473 | 2 |
| #12997 | 17 |