Finite Group DatabasebetaFinite Group DatabasebetaOrder 26944.
262 conjugacy classes of subgroups; only the 107 normal subgroups are shown.
This group has 262 conjugacy classes of subgroups — too many to draw. Only its 107 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 |
|---|---|---|
| 1. C2×#20269771 | C2 | semidirect |
| 2. #27212397 | C2 | semidirect |
| 3. #27212396 | C2 | semidirect |
| 4. #27212392 | C2 | semidirect |
| 5. #27212391 | C2 | semidirect |
| 6. #27212386 | C2 | semidirect |
| 7. C2×#20269755 | C2 | semidirect |
| 8. C2×#41×C421 | C2 | semidirect |
| 12. #20269771 | C22 | semidirect |
| 13. C2×Dic842 | C22 | semidirect |
| 14. C2×D1684 | C22 | semidirect |
| 17. #20269761 | C22 | semidirect |
| 18. #20269759 | C22 | semidirect |
| 19. #20269758 | C22 | semidirect |
| 20. #20269756 | C22 | semidirect |
| 21. #20269755 | C22 | semidirect |
| 22. #20269755 | C22 | semidirect |
| 23. C2×#16809890 | C22 | semidirect |
| 27. #41×C421 | C22 | semidirect |
| 28. C2×Q8×C421 | C22 | semidirect |
| 30. C2×D4×C421 | C22 | semidirect |
| 81. C421 | #575 | semidirect |
| 84. C2×#41 | D421 | semidirect |
| 98. #41 | C2×D421 | semidirect |
| 100. C2×Q8 | C2×D421 | semidirect |
| 104. C2×D4 | C2×D421 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#20269771 | 2 |
| #27212397 | 2 |
| #27212396 | 2 |
| #27212392 | 2 |
| #27212391 | 2 |
| #27212386 | 2 |
| C2×#20269755 | 2 |
| C2×#41×C421 | 2 |
| #575 | 421 |