Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×#3866 | C2 | semidirect |
| 3. (C2×#3866)⋊Q8 | C2 | semidirect |
| 5. #14558483 | C2 | semidirect |
| 6. #14558480 | C2 | semidirect |
| 7. #14558479 | C2 | semidirect |
| 8. #14558469 | C2 | semidirect |
| 27. #11924525 | C4 | semidirect |
| 28. #11924524 | C4 | semidirect |
| 29. #11924523 | C4 | semidirect |
| 30. #11924522 | C4 | semidirect |
| 33. #124×C37 | C4 | semidirect |
| 42. C2×Q8×C37 | C2×C4 | semidirect |
| 53. C2×Dic74 | C2×C4 | semidirect |
| 54. C2×Dic74 | C2×C4 | semidirect |
| 64. C22⋊C4×C37 | C2×C4 | semidirect |
| 65. C42×C37 | C2×C4 | semidirect |
| 66. C22⋊Dic37 | C2×C4 | semidirect |
| 67. #10596938 | C2×C4 | semidirect |
| 68. #10596938 | C2×C4 | semidirect |
| 69. C4×Dic37 | C2×C4 | semidirect |
| 70. C4×Dic37 | C2×C4 | semidirect |
| 148. C37 | #2326 | semidirect |
| 156. #124 | #3866 | semidirect |
| 178. C2×Q8 | C2×#3866 | semidirect |
| 203. C22⋊C4 | C2×#3866 | semidirect |
| 209. C42 | C2×#3866 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#3866 | 2 |
| C2×D4×#3866 | 2 |
| (C2×#3866)⋊Q8 | 2 |
| #14558485 | 2 |
| #14558483 | 2 |
| #14558480 | 2 |
| #14558479 | 2 |
| #14558469 | 2 |
| #124×D37 | 2 |
| #2326 | 37 |