Finite Group DatabasebetaFinite Group DatabasebetaOrder 17536.
5796 conjugacy classes of subgroups; only the 3201 normal subgroups are shown.
This group has 5796 conjugacy classes of subgroups — too many to draw. Only its 3201 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C25×D137 |
| commutator, socle, cosocle | C2×C137 | C26 |
| Fitting | C2×2−1+4×C137 | C2 |
| hypercenter | C2×2−1+4 | D137 |
| hypocenter | C137 | 2−1+6 |
| LCS | G ▷ C2×C137 ▷ C137 | |
| UCS | C1 ◁ C2 ◁ C2×2−1+4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #22578240 | C2 | semidirect |
| 2. #22578239 | C2 | semidirect |
| 3. C2×#17984136 | C2 | semidirect |
| 4. 2−1+4×D137 | C2 | semidirect |
| 5. C2×2−1+4×C137 | C2 | semidirect |
| 6. #17984136 | C22 | semidirect |
| 7. #17984136 | C22 | semidirect |
| 8. #17984135 | C22 | semidirect |
| 9. #17984134 | C22 | semidirect |
| 10. #17984133 | C22 | semidirect |
| 11. C2×#14555511 | C22 | semidirect |
| 12. C2×#14555510 | C22 | semidirect |
| 13. #41×D137 | C22 | semidirect |
| 14. C2×Q8×D137 | C22 | semidirect |
| 15. 2−1+4×C137 | C22 | semidirect |
| 16. C2×#41×C137 | C22 | semidirect |
| 17. C22×Q8×C137 | C22 | semidirect |
| 56. C137 | 2−1+6 | semidirect |
| 62. C2×2−1+4 | D137 | semidirect |
| 66. 2−1+4 | C2×D137 | semidirect |
| 72. C2×#41 | C2×D137 | semidirect |
| 74. C22×Q8 | C2×D137 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #22578240 | 2 |
| #22578239 | 2 |
| C2×#17984136 | 2 |
| 2−1+4×D137 | 2 |
| C2×2−1+4×C137 | 2 |
| 2−1+6 | 137 |