Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
486 conjugacy classes of subgroups; only the 184 normal subgroups are shown.
This group has 486 conjugacy classes of subgroups — too many to draw. Only its 184 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 |
|---|---|---|
| 3. C2×#11763697 | C2 | semidirect |
| 4. #14543822 | C2 | semidirect |
| 7. C22×#63216 | C4 | semidirect |
| 11. C22⋊#63216 | C4 | semidirect |
| 65. #63216 | C22⋊C4 | semidirect |
| 97. C22×C17 | #346 | semidirect |
| 146. C17 | #12611 | semidirect |
| 198. C22 | #11763697 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63216 | 2 |
| C2×C22⋊#63216 | 2 |
| C2×#11763697 | 2 |
| #14543822 | 2 |
| C22⋊C4×#3622 | 2 |
| #12611 | 17 |