Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
188 conjugacy classes of subgroups; only the 57 normal subgroups are shown.
This group has 188 conjugacy classes of subgroups — too many to draw. Only its 57 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 | C22×D39 |
| commutator, socle, cosocle | C22×C3×C13 | C23 |
| Fitting | C3×C13×C4⋊C4 | C2 |
| hypercenter | C4⋊C4 | D39 |
| hypocenter | C3×C13 | #121 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C4⋊C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×D156 | C2 | semidirect |
| 2. C2×D156 | C2 | semidirect |
| 3. C2×C4×D39 | C2 | semidirect |
| 4. C3×C13×C4⋊C4 | C2 | semidirect |
| 5. #10597666 | C2 | semidirect |
| 18. C13×C4⋊C4 | D3 | semidirect |
| 26. C2×D39 | D4 | semidirect |
| 28. C3×C4×C13 | D4 | semidirect |
| 52. C4×C13 | D12 | semidirect |
| 57. C3×C4⋊C4 | D13 | semidirect |
| 59. C3×C13 | #121 | semidirect |
| 77. C4⋊C4 | D39 | semidirect |
| 79. C13 | #895 | semidirect |
| 88. C3×C4 | D52 | semidirect |
| 112. C4 | D156 | semidirect |
| 113. C3 | #88149 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×D156 | 2 |
| C2×C4×D39 | 2 |
| C3×C13×C4⋊C4 | 2 |
| #10597666 | 2 |
| #88149 | 3 |
| #895 | 13 |