Finite Group DatabasebetaFinite Group DatabasebetaOrder 33344.
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×#22552364 | C2 | semidirect |
| 2. #30659739 | C2 | semidirect |
| 3. #30659738 | C2 | semidirect |
| 4. #30659734 | C2 | semidirect |
| 5. #30659733 | C2 | semidirect |
| 6. #30659728 | C2 | semidirect |
| 7. C2×#22552348 | C2 | semidirect |
| 8. C2×#41×C521 | C2 | semidirect |
| 12. #22552364 | C22 | semidirect |
| 13. C2×Dic1042 | C22 | semidirect |
| 14. C2×D2084 | C22 | semidirect |
| 17. #22552354 | C22 | semidirect |
| 18. #22552352 | C22 | semidirect |
| 19. #22552351 | C22 | semidirect |
| 20. #22552349 | C22 | semidirect |
| 21. #22552348 | C22 | semidirect |
| 22. #22552348 | C22 | semidirect |
| 23. C2×#16861960 | C22 | semidirect |
| 27. #41×C521 | C22 | semidirect |
| 28. C2×Q8×C521 | C22 | semidirect |
| 30. C2×D4×C521 | C22 | semidirect |
| 81. C521 | #575 | semidirect |
| 84. C2×#41 | D521 | semidirect |
| 98. #41 | C2×D521 | semidirect |
| 100. C2×Q8 | C2×D521 | semidirect |
| 104. C2×D4 | C2×D521 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#22552364 | 2 |
| #30659739 | 2 |
| #30659738 | 2 |
| #30659734 | 2 |
| #30659733 | 2 |
| #30659728 | 2 |
| C2×#22552348 | 2 |
| C2×#41×C521 | 2 |
| #575 | 521 |