Finite Group DatabasebetaFinite Group DatabasebetaOrder 26816.
152 conjugacy classes of subgroups; only the 58 normal subgroups are shown.
This group has 152 conjugacy classes of subgroups — too many to draw. Only its 58 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 | C2×D4 |
| commutator, Frattini, cosocle | C2×C4 | C23×C419 |
| prime radical | C2×#41×C419 | C2 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C22×C419 ◁ C22×C4×C419 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×Q16×C419 | C2 | semidirect |
| 3. C2×SD16×C419 | C2 | semidirect |
| 4. C22⋊Q8×C419 | C2 | semidirect |
| 5. #103×C419 | C2 | semidirect |
| 6. #102×C419 | C2 | semidirect |
| 7. C22⋊C8×C419 | C2 | semidirect |
| 60. C419 | #452 | direct (N × H) |
| 61. #452 | C419 | direct (N × H) |
| 63. C2×Q16 | C2×C419 | semidirect |
| 64. C2×SD16 | C2×C419 | semidirect |
| 65. C22⋊Q8 | C2×C419 | semidirect |
| 66. #103 | C2×C419 | semidirect |
| 67. #102 | C2×C419 | semidirect |
| 68. C22⋊C8 | C2×C419 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#41×C419 | 2 |
| C2×Q16×C419 | 2 |
| C2×SD16×C419 | 2 |
| C22⋊Q8×C419 | 2 |
| #103×C419 | 2 |
| #102×C419 | 2 |
| C22⋊C8×C419 | 2 |
| #452 | 419 |