Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
1598 conjugacy classes of subgroups.
The subgroup lattice has 350 nodes — too large to display as a diagram.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C67 | C25 |
| commutator, Frattini, cosocle | C23 | C25×C67 |
| prime radical | C24×C67 | C24 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C23×C67 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. C67×#2612 | C2 | semidirect |
| 5. C67×#2606 | C2 | semidirect |
| 6. C67×#2605 | C2 | semidirect |
| 59. C2×C42×C67 | Q8 | semidirect |
| 168. #35120 | C67 | direct (N × H) |
| 178. #2612 | C2×C67 | semidirect |
| 179. #2606 | C2×C67 | semidirect |
| 180. #2605 | C2×C67 | semidirect |
| 184. C67 | #35120 | direct (N × H) |
| 234. C2×C42 | Q8×C67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C67×#2855 | 2 |
| C67×#2659 | 2 |
| C67×#2646 | 2 |
| C67×#2612 | 2 |
| C67×#2606 | 2 |
| C67×#2605 | 2 |
| C67×#2329 | 2 |
| C67×#2283 | 2 |
| C2×#376×C67 | 2 |
| #35120 | 67 |