Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 188 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×D52 | C2 | semidirect |
| 2. C2×C3×D52 | C2 | semidirect |
| 3. C2×C3×C4×D13 | C2 | semidirect |
| 4. C3×C13×C4⋊C4 | C2 | semidirect |
| 5. C3×#6103 | C2 | semidirect |
| 6. #88149 | C3 | direct (N × H) |
| 15. C2×D52 | C2×C3 | semidirect |
| 16. C2×D52 | C2×C3 | semidirect |
| 17. C2×C4×D13 | C2×C3 | semidirect |
| 18. C13×C4⋊C4 | C2×C3 | semidirect |
| 19. #6103 | C2×C3 | semidirect |
| 26. C2×C3×D13 | D4 | semidirect |
| 28. C3×C4×C13 | D4 | semidirect |
| 50. C2×D13 | C3×D4 | semidirect |
| 52. C4×C13 | C3×D4 | semidirect |
| 57. C3×C4⋊C4 | D13 | semidirect |
| 59. C3×C13 | #121 | semidirect |
| 77. C4⋊C4 | C3×D13 | semidirect |
| 79. C13 | C3×#121 | semidirect |
| 89. C3×C4 | D52 | semidirect |
| 112. C4 | C3×D52 | semidirect |
| 113. C3 | #88149 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D52 | 2 |
| C2×C3×C4×D13 | 2 |
| C3×C13×C4⋊C4 | 2 |
| C3×#6103 | 2 |
| #88149 | 3 |
| C3×#121 | 13 |