Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
148 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 148 conjugacy classes of subgroups — too many to draw. Only its 54 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, prime radical | C23×C3×C13 | C22 |
| hypercenter | C23 | D3×D13 |
| hypocenter | C3×C13 | C22⋊Q8 |
| 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 |
|---|---|---|
| 2. C2×#64605 | C2 | semidirect |
| 5. Dic3⋊Dic13 | C2 | semidirect |
| 6. #10597612 | C2 | semidirect |
| 7. #10597611 | C2 | semidirect |
| 27. C22×C3×C13 | Q8 | semidirect |
| 51. C22×C13 | Dic6 | semidirect |
| 66. C3×C13 | C22⋊Q8 | semidirect |
| 88. C13 | #878 | semidirect |
| 91. C22×C3 | Dic26 | semidirect |
| 114. C22 | #64605 | semidirect |
| 122. C3 | #88132 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×Dic39 | 2 |
| C2×#64605 | 2 |
| C13×#217 | 2 |
| C3×C22⋊Dic13 | 2 |
| Dic3⋊Dic13 | 2 |
| #10597612 | 2 |
| #10597611 | 2 |
| #88132 | 3 |
| #878 | 13 |