Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 56 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 56 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C2×D3×D13 |
| commutator, socle, cosocle | C22×C3×C13 | C23 |
| Fitting | C23×C3×C13 | C22 |
| hypercenter | C23 | D3×D13 |
| hypocenter | C3×C13 | #121 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C23 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#64625 | C2 | semidirect |
| 2. C2×C13×#67 | C2 | semidirect |
| 3. C22×C3×Dic13 | C2 | semidirect |
| 4. C2×#64604 | C2 | semidirect |
| 5. #10597611 | C2 | semidirect |
| 6. #10597610 | C2 | semidirect |
| 7. (C2×D3)⋊Dic13 | C2 | semidirect |
| 23. C22×Dic13 | D3 | semidirect |
| 29. C22×C3×C13 | D4 | semidirect |
| 39. C3×Dic13 | D4 | semidirect |
| 64. C22×C13 | D12 | semidirect |
| 72. Dic13 | #67 | semidirect |
| 75. C2×#67 | D13 | semidirect |
| 80. C3×C13 | #121 | semidirect |
| 106. C13 | #930 | semidirect |
| 109. C22×C3 | C22⋊D13 | semidirect |
| 146. C22 | #64604 | semidirect |
| 152. C3 | #88193 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#64625 | 2 |
| C2×C13×#67 | 2 |
| C22×C3×Dic13 | 2 |
| C2×#64604 | 2 |
| #10597611 | 2 |
| #10597610 | 2 |
| (C2×D3)⋊Dic13 | 2 |
| #88193 | 3 |
| #930 | 13 |