Finite Group DatabasebetaFinite Group DatabasebetaOrder 4352.
878 conjugacy classes of subgroups; only the 239 normal subgroups are shown.
This group has 878 conjugacy classes of subgroups — too many to draw. Only its 239 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. #14528402 | C2 | semidirect |
| 4. #14528401 | C2 | semidirect |
| 5. #14528400 | C2 | semidirect |
| 7. C17×#1713 | C2 | semidirect |
| 67. C8×D17 | Q16 | semidirect |
| 83. C8×C17 | C2×Q16 | semidirect |
| 85. #3622 | C2×Q16 | semidirect |
| 91. #1713 | D17 | direct (N × H) |
| 120. D17 | #1713 | direct (N × H) |
| 143. C17 | C2×#1713 | semidirect |
| 182. C8 | Q16×D17 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D17×#500 | 2 |
| D17×#494 | 2 |
| #14528402 | 2 |
| #14528401 | 2 |
| #14528400 | 2 |
| C82×D17 | 2 |
| C17×#1713 | 2 |
| C2×#1713 | 17 |