Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
552 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 552 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. C2×#16863832 | C2 | semidirect |
| 2. #22569929 | C2 | semidirect |
| 3. C2×#16863209 | C2 | semidirect |
| 4. #22561944 | C2 | semidirect |
| 5. #22561837 | C2 | semidirect |
| 6. #22558325 | C2 | semidirect |
| 7. C67×#3058 | C2 | semidirect |
| 41. C2×Dic268 | D4 | semidirect |
| 43. C2×D536 | D4 | semidirect |
| 50. #14523983 | D4 | semidirect |
| 54. #14523979 | D4 | semidirect |
| 214. #3058 | D67 | semidirect |
| 219. C67 | #13310 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863832 | 2 |
| #22569929 | 2 |
| C2×#16863209 | 2 |
| #22561944 | 2 |
| #22561837 | 2 |
| #22558325 | 2 |
| C67×#3058 | 2 |
| #13310 | 67 |