Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
370 conjugacy classes of subgroups; only the 97 normal subgroups are shown.
This group has 370 conjugacy classes of subgroups — too many to draw. Only its 97 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. #14558016 | C2 | semidirect |
| 2. C2×#11924463 | C2 | semidirect |
| 3. #14557538 | C2 | semidirect |
| 4. #14557436 | C2 | semidirect |
| 5. #14557301 | C2 | semidirect |
| 6. #14557294 | C2 | semidirect |
| 24. AGL(1,ℤ/8)×C37 | C4 | semidirect |
| 40. C2×D4×C37 | C2×C4 | semidirect |
| 50. M16×C37 | C2×C4 | semidirect |
| 75. Q8×C37 | C22⋊C4 | semidirect |
| 83. D4×C37 | C22⋊C4 | semidirect |
| 140. C37 | #1883 | semidirect |
| 144. AGL(1,ℤ/8) | Dic37 | semidirect |
| 173. C2×D4 | C2×Dic37 | semidirect |
| 185. M16 | C2×Dic37 | semidirect |
| 208. Q8 | C22⋊Dic37 | semidirect |
| 216. D4 | C22⋊Dic37 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #14558016 | 2 |
| C2×#11924463 | 2 |
| #14557538 | 2 |
| #14557436 | 2 |
| #14557301 | 2 |
| #14557294 | 2 |
| C2×AGL(1,ℤ/8)×C37 | 2 |
| #1883 | 37 |