Finite Group DatabasebetaFinite Group DatabasebetaOrder 3712.
572 conjugacy classes of subgroups; only the 173 normal subgroups are shown.
This group has 572 conjugacy classes of subgroups — too many to draw. Only its 173 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×#11745266 | C2 | semidirect |
| 2. #14271713 | C2 | semidirect |
| 3. #14271547 | C2 | semidirect |
| 4. #14271543 | C2 | semidirect |
| 5. #14271540 | C2 | semidirect |
| 6. #14271536 | C2 | semidirect |
| 7. C2×C4×C8×C29 | C2 | semidirect |
| 31. C2×C8×C29 | D4 | semidirect |
| 66. C4×C29 | #135 | semidirect |
| 75. C2×C4×C8 | D29 | semidirect |
| 95. C29 | #3147 | semidirect |
| 107. C2×C8 | D116 | semidirect |
| 139. C4 | #11745266 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#11745266 | 2 |
| #14271713 | 2 |
| #14271547 | 2 |
| #14271543 | 2 |
| #14271540 | 2 |
| #14271536 | 2 |
| C2×C4×C8×C29 | 2 |
| #3147 | 29 |