Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
430 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 430 conjugacy classes of subgroups — too many to draw. Only its 115 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. C2×#16863216 | C2 | semidirect |
| 5. #22560364 | C2 | semidirect |
| 6. #22558309 | C2 | semidirect |
| 7. C67×#1383 | C2 | semidirect |
| 12. #16863512 | C4 | semidirect |
| 70. Dic268 | C4⋊C4 | semidirect |
| 74. D536 | C4⋊C4 | semidirect |
| 157. #1383 | D67 | semidirect |
| 158. C67 | #12823 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863512 | 2 |
| C2×#16863216 | 2 |
| C2×#16863207 | 2 |
| C2×#16863205 | 2 |
| #22560364 | 2 |
| #22558309 | 2 |
| C67×#1383 | 2 |
| #12823 | 67 |