Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
216 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 216 conjugacy classes of subgroups — too many to draw. Only its 76 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. #14545171 | C2 | semidirect |
| 2. #14543819 | C2 | semidirect |
| 3. #14543746 | C2 | semidirect |
| 4. C16×#3624 | C2 | semidirect |
| 24. C17×Q32 | C8 | semidirect |
| 25. C17×SD32 | C8 | semidirect |
| 26. C17×D16 | C8 | semidirect |
| 89. Q32 | #3624 | semidirect |
| 90. SD32 | #3624 | semidirect |
| 91. D16 | #3624 | semidirect |
| 103. C17 | #12046 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14545171 | 2 |
| #14543819 | 2 |
| #14543746 | 2 |
| C16×#3624 | 2 |
| #14530665 | 2 |
| #12046 | 17 |