Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
422 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 422 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 2. #22561998 | C2 | semidirect |
| 5. #22560953 | C2 | semidirect |
| 6. #22558292 | C2 | semidirect |
| 7. C67×#1386 | C2 | semidirect |
| 21. #16863205 | C4 | semidirect |
| 49. #14523983 | C2×C4 | semidirect |
| 70. #106×C67 | C2×C4 | semidirect |
| 85. Dic268 | C4⋊C4 | semidirect |
| 89. D536 | C4⋊C4 | semidirect |
| 187. #1386 | D67 | semidirect |
| 189. C67 | #12943 | semidirect |
| 245. #106 | C4×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22569009 | 2 |
| #22561998 | 2 |
| C2×#16863205 | 2 |
| #22561922 | 2 |
| #22560953 | 2 |
| #22558292 | 2 |
| C67×#1386 | 2 |
| #12943 | 67 |