Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D419 |
| commutator, socle, cosocle | C22×C419 | C24 |
| Fitting | C2×#41×C419 | C2 |
| hypercenter | C2×#41 | D419 |
| hypocenter | C419 | #547 |
| LCS | G ▷ C22×C419 ▷ C419 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#20269410 | C2 | semidirect |
| 2. #27211716 | C2 | semidirect |
| 3. #27211701 | C2 | semidirect |
| 4. #27211699 | C2 | semidirect |
| 5. #27211697 | C2 | semidirect |
| 6. #27211694 | C2 | semidirect |
| 7. #27211690 | C2 | semidirect |
| 8. D4×Dic419 | C2 | semidirect |
| 9. C4×C22⋊D419 | C2 | semidirect |
| 10. C2×Dic419⋊C4 | C2 | semidirect |
| 11. C2×#41×C419 | C2 | semidirect |
| 53. D4×C419 | D4 | semidirect |
| 76. Dic419 | #41 | semidirect |
| 83. C419 | #547 | semidirect |
| 86. C2×#41 | D419 | semidirect |
| 129. D4 | C22⋊D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269410 | 2 |
| #27211716 | 2 |
| #27211701 | 2 |
| #27211699 | 2 |
| #27211697 | 2 |
| #27211694 | 2 |
| #27211690 | 2 |
| D4×Dic419 | 2 |
| C4×C22⋊D419 | 2 |
| C2×Dic419⋊C4 | 2 |
| C2×#41×C419 | 2 |
| #547 | 419 |