Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1252 conjugacy classes of subgroups; only the 179 normal subgroups are shown.
This group has 1252 conjugacy classes of subgroups — too many to draw. Only its 179 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. #22570662 | C2 | semidirect |
| 2. #22559498 | C2 | semidirect |
| 3. #22558801 | C2 | semidirect |
| 4. C67×#3549 | C2 | semidirect |
| 6. C2×#14524040 | C22 | semidirect |
| 7. #16863786 | C22 | semidirect |
| 10. C4×#11761612 | C22 | semidirect |
| 11. #16863136 | C22 | semidirect |
| 12. H(3,𝔽4)×C67 | C22 | semidirect |
| 97. #3549 | D67 | semidirect |
| 101. C67 | #19073 | semidirect |
| 103. H(3,𝔽4) | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22570662 | 2 |
| #22559498 | 2 |
| #22558801 | 2 |
| C67×#3549 | 2 |
| #19073 | 67 |