Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
292 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2 | C22×D3×D13 |
| commutator, socle, cosocle | C2×C3×C13 | C24 |
| Fitting | C2×C3×C4×C13 | C22 |
| hypercenter | C2×C4 | D3×D13 |
| hypocenter | C3×C13 | 2−1+4 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C2 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×Dic78 | C2 | semidirect |
| 2. C13×#235 | C2 | semidirect |
| 3. C3×#6127 | C2 | semidirect |
| 4. #10597746 | C2 | semidirect |
| 5. #10597738 | C2 | semidirect |
| 6. D3×Dic26 | C2 | semidirect |
| 7. #10597731 | C2 | semidirect |
| 8. Dic6×D13 | C2 | semidirect |
| 31. #6127 | D3 | semidirect |
| 76. #235 | D13 | semidirect |
| 79. C3×C13 | 2−1+4 | semidirect |
| 109. C13 | #1010 | semidirect |
| 146. C3 | #88257 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Dic78 | 2 |
| C13×#235 | 2 |
| C3×#6127 | 2 |
| #10597746 | 2 |
| #10597738 | 2 |
| D3×Dic26 | 2 |
| #10597731 | 2 |
| Dic6×D13 | 2 |
| #88257 | 3 |
| #1010 | 13 |