Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
250 conjugacy classes of subgroups; only the 104 normal subgroups are shown.
This group has 250 conjugacy classes of subgroups — too many to draw. Only its 104 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. #14543703 | C2 | semidirect |
| 4. #14543700 | C2 | semidirect |
| 59. C16×C17 | M16 | semidirect |
| 61. #63214 | M16 | semidirect |
| 135. C17 | #11413 | semidirect |
| 157. C16 | #63247 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545146 | 2 |
| #14543993 | 2 |
| #14543703 | 2 |
| #14543700 | 2 |
| C2×#11762584 | 2 |
| #11413 | 17 |