Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
322 conjugacy classes of subgroups; only the 67 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 67 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C22×D419 |
| commutator, socle, cosocle | C23×C419 | C23 |
| Fitting | C2×C22⋊C4×C419 | C2 |
| hypercenter | C2×C22⋊C4 | D419 |
| hypocenter | C419 | #392 |
| LCS | G ▷ C23×C419 ▷ C419 | |
| UCS | C1 ◁ C23 ◁ C2×C22⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D1676 | C2 | semidirect |
| 2. C22×C22⋊D419 | C2 | semidirect |
| 3. C2×(C2×D419)⋊C4 | C2 | semidirect |
| 4. C419⋊#95 | C2 | semidirect |
| 5. C2×C22⋊C4×C419 | C2 | semidirect |
| 24. C22×D419 | D4 | semidirect |
| 29. C2×Dic419 | D4 | semidirect |
| 34. C23×C419 | D4 | semidirect |
| 39. C2×C4×C419 | D4 | semidirect |
| 67. C419 | #392 | semidirect |
| 72. C2×C22⋊C4 | D419 | semidirect |
| 97. C23 | D1676 | semidirect |
| 107. C2×C4 | C22⋊D419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D1676 | 2 |
| C22×C22⋊D419 | 2 |
| C2×(C2×D419)⋊C4 | 2 |
| C419⋊#95 | 2 |
| C2×C22⋊C4×C419 | 2 |
| #392 | 419 |