Finite Group DatabasebetaFinite Group DatabasebetaOrder 17152.
30862 conjugacy classes of subgroups; only the 1323 normal subgroups are shown.
This group has 30862 conjugacy classes of subgroups — too many to draw. Only its 1323 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C24 | C23×D67 |
| commutator | C23×C67 | C23×C4 |
| Fitting, prime radical | C27×C67 | C2 |
| socle, cosocle | C24×C67 | C24 |
| hypercenter | C27 | D67 |
| hypocenter | C67 | #14679 |
| LCS | G ▷ C23×C67 ▷ C67 | |
| UCS | C1 ◁ C24 ◁ C27 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#16863252 | C2 | semidirect |
| 3. C22×C22⋊Dic67 | C22 | semidirect |
| 6. C26×C67 | C4 | semidirect |
| 8. C23×Dic67 | C23 | semidirect |
| 24. C24×C67 | C22⋊C4 | semidirect |
| 42. C22×C67 | #379 | semidirect |
| 52. C67 | #14679 | semidirect |
| 54. C26 | Dic67 | semidirect |
| 72. C24 | C22⋊Dic67 | semidirect |
| 92. C22 | #16863252 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#16863252 | 2 |
| C27×C67 | 2 |
| #14679 | 67 |