Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
578 conjugacy classes of subgroups; only the 137 normal subgroups are shown.
This group has 578 conjugacy classes of subgroups — too many to draw. Only its 137 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. C23×#63241 | C2 | semidirect |
| 2. C2×#11763906 | C2 | semidirect |
| 3. C2×C22⋊#63241 | C2 | semidirect |
| 4. #14545854 | C2 | semidirect |
| 42. C2×#63241 | D4 | semidirect |
| 60. C2×C22⋊D17 | C16 | semidirect |
| 106. C22×D17 | C2×C16 | semidirect |
| 119. C2×Dic17 | C2×C16 | semidirect |
| 142. C22×C17 | C22⋊C16 | semidirect |
| 215. C17 | #12976 | semidirect |
| 303. C22 | #11763906 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×#63241 | 2 |
| C2×#11763906 | 2 |
| C2×C22⋊#63241 | 2 |
| #14545854 | 2 |
| C2×#11763836 | 2 |
| #12976 | 17 |