Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
576 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 576 conjugacy classes of subgroups — too many to draw. Only its 250 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 |
|---|---|---|
| 2. #14272167 | C2 | direct (N × H) |
| 3. C2×C4⋊#6599 | C2 | semidirect |
| 15. C4⋊#6599 | C22 | semidirect |
| 39. C2×C4×C29 | M16 | semidirect |
| 61. C4×C29 | C2×M16 | semidirect |
| 70. C2×C29 | #423 | semidirect |
| 85. C29 | C2×#423 | semidirect |
| 118. C2×C4 | #90796 | semidirect |
| 133. C4 | C2×#90796 | semidirect |
| 136. C2 | #14272167 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#90796 | 2 |
| #14272167 | 2 |
| C2×C4⋊#6599 | 2 |
| C2×C42×D29 | 2 |
| C2×#423 | 29 |