Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 70 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×C3×Q8×C13 | C2 | semidirect |
| 4. C3×C4⋊Dic13 | C2 | semidirect |
| 5. C3×#6101 | C2 | semidirect |
| 6. #88200 | C3 | direct (N × H) |
| 14. C2×Q8×C13 | C2×C3 | semidirect |
| 17. C4⋊Dic13 | C2×C3 | semidirect |
| 18. #6101 | C2×C3 | semidirect |
| 22. C2×C3×D13 | Q8 | semidirect |
| 42. C2×D13 | C3×Q8 | semidirect |
| 47. C2×C3×Q8 | D13 | semidirect |
| 52. C3×C13 | C22⋊Q8 | semidirect |
| 65. C2×Q8 | C3×D13 | semidirect |
| 70. C13 | C3×C22⋊Q8 | semidirect |
| 98. C3 | #88200 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×C13 | 2 |
| C2×C3×C4×D13 | 2 |
| C3×#6103 | 2 |
| C3×C4⋊Dic13 | 2 |
| C3×#6101 | 2 |
| #88200 | 3 |
| C3×C22⋊Q8 | 13 |