Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
228 conjugacy classes of subgroups; only the 166 normal subgroups are shown.
This group has 228 conjugacy classes of subgroups — too many to draw. Only its 166 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C419 | C24 |
| commutator, Frattini, cosocle | C22 | C24×C419 |
| prime radical | C2×D4×C419 | C22 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C419 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C4⋊Q8×C419 | C2 | semidirect |
| 2. #125×C419 | C2 | semidirect |
| 3. C22⋊Q8×C419 | C2 | semidirect |
| 4. C22⋊Q8×C419 | C2 | semidirect |
| 5. C4×Q8×C419 | C2 | semidirect |
| 8. C2×C4⋊C4×C419 | C2 | semidirect |
| 28. D4×C419 | Q8 | semidirect |
| 53. C419 | #554 | direct (N × H) |
| 54. #554 | C419 | direct (N × H) |
| 55. C4⋊Q8 | C2×C419 | semidirect |
| 56. #125 | C2×C419 | semidirect |
| 57. C22⋊Q8 | C2×C419 | semidirect |
| 58. C22⋊Q8 | C2×C419 | semidirect |
| 59. C4×Q8 | C2×C419 | semidirect |
| 62. C2×C4⋊C4 | C2×C419 | semidirect |
| 82. D4 | Q8×C419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C4⋊Q8×C419 | 2 |
| #125×C419 | 2 |
| C22⋊Q8×C419 | 2 |
| C4×Q8×C419 | 2 |
| C4×D4×C419 | 2 |
| C2×C4⋊C4×C419 | 2 |
| #554 | 419 |