Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
1252 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 179 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. #14539237 | C2 | semidirect |
| 2. #14528073 | C2 | semidirect |
| 3. #14527376 | C2 | semidirect |
| 4. C17×#3549 | C2 | semidirect |
| 6. C2×#10587560 | C22 | semidirect |
| 7. #11763199 | C22 | semidirect |
| 10. C4×#63223 | C22 | semidirect |
| 11. #11762549 | C22 | semidirect |
| 12. C17×H(3,𝔽4) | C22 | semidirect |
| 83. #3549 | D17 | semidirect |
| 98. H(3,𝔽4) | C2×D17 | semidirect |
| 136. C17 | #19073 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14539237 | 2 |
| #14528073 | 2 |
| #14527376 | 2 |
| C17×#3549 | 2 |
| #19073 | 17 |