Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
478 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 478 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14545908 | C2 | semidirect |
| 2. #14545905 | C2 | semidirect |
| 4. #14545899 | C2 | semidirect |
| 6. #14545893 | C2 | semidirect |
| 61. C2×SD16×C17 | C8 | semidirect |
| 62. C2×#63230 | C8 | semidirect |
| 63. C2×#63229 | C8 | semidirect |
| 68. C2×#63219 | C8 | semidirect |
| 263. C2×SD16 | #3633 | semidirect |
| 302. C17 | #9667 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545908 | 2 |
| #14545905 | 2 |
| #14545904 | 2 |
| #14545899 | 2 |
| #14545898 | 2 |
| #14545893 | 2 |
| C2×SD16×#595 | 2 |
| #9667 | 17 |