Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
456 conjugacy classes of subgroups; only the 175 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 175 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 |
|---|---|---|
| 3. #14557641 | C2 | semidirect |
| 4. #14557640 | C2 | semidirect |
| 5. #14557639 | C2 | semidirect |
| 6. C4×#10596942 | C2 | semidirect |
| 7. #14557625 | C2 | semidirect |
| 11. C37×#441 | C2 | semidirect |
| 15. Q16×D37 | C4 | semidirect |
| 114. #441 | D37 | semidirect |
| 120. C37 | #2950 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q16×D37 | 2 |
| #14558009 | 2 |
| #14557641 | 2 |
| #14557640 | 2 |
| #14557639 | 2 |
| C4×#10596942 | 2 |
| #14557625 | 2 |
| #14557568 | 2 |
| #14557540 | 2 |
| #14557490 | 2 |
| C37×#441 | 2 |
| #2950 | 37 |