Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
412 conjugacy classes of subgroups; only the 145 normal subgroups are shown.
This group has 412 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. #14558090 | C2 | semidirect |
| 2. #14557929 | C2 | semidirect |
| 3. #14557905 | C2 | semidirect |
| 4. #14557885 | C2 | semidirect |
| 5. #14557879 | C2 | semidirect |
| 6. #14557760 | C2 | semidirect |
| 7. C4×#10596940 | C2 | semidirect |
| 8. C2×C4×#64436 | C2 | semidirect |
| 78. C2×C4×C37 | SD16 | semidirect |
| 90. #64436 | #41 | semidirect |
| 122. C37 | #3167 | semidirect |
| 195. C2×C4 | #10596940 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558090 | 2 |
| #14557929 | 2 |
| #14557905 | 2 |
| #14557885 | 2 |
| #14557879 | 2 |
| #14557760 | 2 |
| C4×#10596940 | 2 |
| C2×C4×#64436 | 2 |
| C37×#532 | 2 |
| #3167 | 37 |