Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
620 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 620 conjugacy classes of subgroups — too many to draw. Only its 125 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×#11745185 | C2 | semidirect |
| 2. #14271164 | C2 | semidirect |
| 3. C2×#11745181 | C2 | semidirect |
| 4. #14271066 | C2 | semidirect |
| 8. C29×H(5,𝔽2) | C4 | semidirect |
| 15. C2×C4⋊Dic29 | C22 | semidirect |
| 16. C2×C4×Dic29 | C22 | semidirect |
| 17. C2×#90777 | C22 | semidirect |
| 64. Q8×C29 | C22⋊C4 | semidirect |
| 71. D4×C29 | C22⋊C4 | semidirect |
| 120. H(5,𝔽2) | Dic29 | semidirect |
| 134. C29 | #1792 | semidirect |
| 177. Q8 | C22⋊Dic29 | semidirect |
| 184. D4 | C22⋊Dic29 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745185 | 2 |
| #14271164 | 2 |
| C2×#11745181 | 2 |
| #14271066 | 2 |
| C2×C29×H(5,𝔽2) | 2 |
| #1792 | 29 |