Finite Group DatabasebetaFinite Group DatabasebetaOrder 4736.
180 conjugacy classes of subgroups; only the 89 normal subgroups are shown.
This group has 180 conjugacy classes of subgroups — too many to draw. Only its 89 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. Q8×#64436 | C2 | semidirect |
| 3. #14557284 | C2 | semidirect |
| 4. Q8⋊#64436 | C2 | semidirect |
| 6. C8×#64436 | C2 | semidirect |
| 26. SD16×C37 | C8 | semidirect |
| 43. Q8×C37 | C2×C8 | semidirect |
| 55. C8×C37 | C2×C8 | semidirect |
| 60. #64436 | SD16 | direct (N × H) |
| 85. C37 | C8×SD16 | semidirect |
| 104. SD16 | #64436 | direct (N × H) |
| 121. Q8 | C2×#64436 | semidirect |
| 138. C8 | C2×#64436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×#64436 | 2 |
| D4×#64436 | 2 |
| #14557284 | 2 |
| Q8⋊#64436 | 2 |
| D4⋊#64436 | 2 |
| C8×#64436 | 2 |
| C4×SD16×C37 | 2 |
| C8×SD16 | 37 |