Order 21088.
164 conjugacy classes of subgroups.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D659 |
| commutator, cosocle | C2×C659 | C24 |
| Frattini | C2 | C23×D659 |
| Fitting | C2×Q8×C659 | C2 |
| socle | C22×C659 | C23 |
| hypercenter | C2×Q8 | D659 |
| hypocenter | C659 | C2×#41 |
| LCS | G ▷ C2×C659 ▷ C659 | |
| UCS | C1 ◁ C22 ◁ C2×Q8 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #24902111 | C2 | direct (N × H) |
| 2. C2×D2636 | C2 | semidirect |
| 3. C2×C4×D659 | C2 | semidirect |
| 4. C2×Q8×C659 | C2 | semidirect |
| 6. D2636 | C22 | semidirect |
| 8. C4×D659 | C22 | semidirect |
| 9. Q8×C659 | C22 | semidirect |
| 16. C2×C659 | #41 | semidirect |
| 19. C659 | C2×#41 | semidirect |
| 22. C2×Q8 | D659 | semidirect |
| 26. Q8 | C2×D659 | semidirect |
| 37. C2 | #24902111 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #24902111 | 2 |
| C2×D2636 | 2 |
| C2×C4×D659 | 2 |
| C2×Q8×C659 | 2 |
| C2×#41 | 659 |