Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
552 conjugacy classes of subgroups; only the 157 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 157 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×#11924567 | C2 | semidirect |
| 3. #14557925 | C2 | semidirect |
| 4. #14557912 | C2 | semidirect |
| 5. #14557907 | C2 | semidirect |
| 6. C4×#10596934 | C2 | semidirect |
| 7. C2×C4⋊Q8×C37 | C2 | semidirect |
| 47. #10596934 | D4 | semidirect |
| 76. C4×C37 | #137 | semidirect |
| 86. C2×C4⋊Q8 | D37 | semidirect |
| 91. C37 | #3152 | semidirect |
| 161. C4 | #11924567 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11924567 | 2 |
| #14558083 | 2 |
| #14557925 | 2 |
| #14557912 | 2 |
| #14557907 | 2 |
| C4×#10596934 | 2 |
| C2×C4⋊Q8×C37 | 2 |
| #3152 | 37 |