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×D4×C13 | C2 | semidirect |
| 2. C2×C13×#67 | C2 | semidirect |
| 3. C2×C13×#67 | C2 | semidirect |
| 4. C22×Dic3×C13 | C2 | semidirect |
| 5. C13×#217 | C2 | semidirect |
| 6. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 7. C13×Dic3⋊C4 | C2 | semidirect |
| 22. C2×D4×C13 | D3 | semidirect |
| 32. C22×C3×C13 | D4 | semidirect |
| 40. Dic3×C13 | D4 | semidirect |
| 52. #939 | C13 | direct (N × H) |
| 67. C22×C13 | #67 | semidirect |
| 73. C2×C3×D4 | C2×C13 | semidirect |
| 74. C2×#67 | C2×C13 | semidirect |
| 75. C2×#67 | C2×C13 | semidirect |
| 76. C22×Dic3 | C2×C13 | semidirect |
| 77. #217 | C2×C13 | semidirect |
| 78. (C2×D3)⋊C4 | C2×C13 | semidirect |
| 79. Dic3⋊C4 | C2×C13 | semidirect |
| 80. C3×C13 | #121 | semidirect |
| 101. C2×D4 | D3×C13 | semidirect |
| 106. C13 | #939 | direct (N × H) |
| 112. C22×C3 | D4×C13 | semidirect |
| 120. Dic3 | D4×C13 | semidirect |
| 146. C22 | C13×#67 | semidirect |
| 152. C3 | C13×#121 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C13 | 2 |
| C2×C13×#67 | 2 |
| C22×Dic3×C13 | 2 |
| C13×#217 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| C13×Dic3⋊C4 | 2 |
| C13×#121 | 3 |
| #939 | 13 |