Finite Group DatabasebetaFinite Group DatabasebetaOrder 4288.
258 conjugacy classes of subgroups; only the 147 normal subgroups are shown.
This group has 258 conjugacy classes of subgroups — too many to draw. Only its 147 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C4 | C23×D67 |
| commutator, socle | C2×C67 | C23×C4 |
| Fitting | #131×C67 | C2 |
| prime radical | #41×D67 | C2 |
| cosocle | C4×C67 | C24 |
| hypercenter | #131 | D67 |
| hypocenter | C67 | #568 |
| LCS | G ▷ C2×C67 ▷ C67 | |
| UCS | C1 ◁ C4 ◁ #131 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #14524051 | C2 | semidirect |
| 3. #14524050 | C2 | semidirect |
| 4. #14524049 | C2 | semidirect |
| 5. C2×#11761611 | C2 | semidirect |
| 6. M16×D67 | C2 | semidirect |
| 7. #131×C67 | C2 | semidirect |
| 14. #11761612 | C22 | semidirect |
| 17. #11761611 | C22 | semidirect |
| 18. #11761611 | C22 | semidirect |
| 19. C2×C67⋊C8 | C22 | semidirect |
| 20. C8×D67 | C22 | semidirect |
| 22. M16×C67 | C22 | semidirect |
| 23. C2×C8×C67 | C22 | semidirect |
| 52. C67 | #568 | semidirect |
| 58. #131 | D67 | semidirect |
| 73. M16 | C2×D67 | semidirect |
| 76. C2×C8 | C2×D67 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×D67 | 2 |
| #14524051 | 2 |
| #14524050 | 2 |
| #14524049 | 2 |
| C2×#11761611 | 2 |
| M16×D67 | 2 |
| #131×C67 | 2 |
| #568 | 67 |