Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
698 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 698 conjugacy classes of subgroups — too many to draw. Only its 145 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×#11924584 | C2 | semidirect |
| 2. #14558331 | C2 | semidirect |
| 3. #14557715 | C2 | semidirect |
| 4. #14557705 | C2 | semidirect |
| 5. #14557551 | C2 | semidirect |
| 6. C2×#11924455 | C2 | semidirect |
| 7. C37×#536 | C2 | semidirect |
| 15. #11924567 | C22 | semidirect |
| 17. #11924562 | C22 | semidirect |
| 21. #11924464 | C22 | semidirect |
| 22. #11924455 | C22 | semidirect |
| 25. C4⋊Q8×C37 | C22 | semidirect |
| 26. #124×C37 | C22 | semidirect |
| 126. #536 | D37 | semidirect |
| 131. C37 | #3020 | semidirect |
| 147. C4⋊Q8 | C2×D37 | semidirect |
| 148. #124 | C2×D37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924584 | 2 |
| #14558331 | 2 |
| #14557715 | 2 |
| #14557705 | 2 |
| #14557551 | 2 |
| C2×#11924455 | 2 |
| C37×#536 | 2 |
| #3020 | 37 |