Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
298 conjugacy classes of subgroups; only the 159 normal subgroups are shown.
This group has 298 conjugacy classes of subgroups — too many to draw. Only its 159 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C2×#20269755 | C2 | semidirect |
| 3. C2×#20269754 | C2 | semidirect |
| 4. M16×D421 | C2 | direct (N × H) |
| 5. C2×C8×D421 | C2 | semidirect |
| 6. C2×M16×C421 | C2 | semidirect |
| 15. #20269755 | C22 | semidirect |
| 16. #20269754 | C22 | semidirect |
| 17. C2×#16809890 | C22 | semidirect |
| 18. C8×D421 | C22 | semidirect |
| 20. M16×C421 | C22 | semidirect |
| 21. C2×C8×C421 | C22 | semidirect |
| 35. #16809890 | C23 | semidirect |
| 41. C8×C421 | C23 | semidirect |
| 47. C2×D421 | M16 | direct (N × H) |
| 56. C2×C421 | C2×M16 | semidirect |
| 59. D421 | C2×M16 | direct (N × H) |
| 60. C421 | C22×M16 | semidirect |
| 66. C2×M16 | D421 | direct (N × H) |
| 79. M16 | C2×D421 | direct (N × H) |
| 82. C2×C8 | C2×D421 | semidirect |
| 102. C8 | C22×D421 | semidirect |
| 119. C2 | M16×D421 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C4×D421 | 2 |
| C2×#20269755 | 2 |
| C2×#20269754 | 2 |
| M16×D421 | 2 |
| C2×C8×D421 | 2 |
| C2×M16×C421 | 2 |
| C22×M16 | 421 |