Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
124 conjugacy classes of subgroups; only the 74 normal subgroups are shown.
This group has 124 conjugacy classes of subgroups — too many to draw. Only its 74 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C419 | C23 |
| commutator | C22 | C22×C4×C419 |
| Frattini, cosocle | C2×C4 | C23×C419 |
| socle | C22×C419 | C22×C4 |
| prime radical | C2×D4×C419 | C4 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C419 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×M16×C419 | C2 | semidirect |
| 2. C22×C8×C419 | C2 | semidirect |
| 4. C4⋊C8×C419 | C2 | semidirect |
| 5. C22⋊C8×C419 | C2 | semidirect |
| 6. C22⋊C8×C419 | C2 | semidirect |
| 7. #97×C419 | C2 | semidirect |
| 36. C8×C419 | D4 | semidirect |
| 42. C22×C419 | M16 | semidirect |
| 55. C419 | #435 | direct (N × H) |
| 56. #435 | C419 | direct (N × H) |
| 57. C2×M16 | C2×C419 | semidirect |
| 58. C22×C8 | C2×C419 | semidirect |
| 60. C4⋊C8 | C2×C419 | semidirect |
| 61. C22⋊C8 | C2×C419 | semidirect |
| 62. C22⋊C8 | C2×C419 | semidirect |
| 63. #97 | C2×C419 | semidirect |
| 92. C8 | D4×C419 | semidirect |
| 98. C22 | M16×C419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×M16×C419 | 2 |
| C22×C8×C419 | 2 |
| C4×D4×C419 | 2 |
| C4⋊C8×C419 | 2 |
| C22⋊C8×C419 | 2 |
| #97×C419 | 2 |
| #435 | 419 |