Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
260 conjugacy classes of subgroups; only the 54 normal subgroups are shown.
This group has 260 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 | C2×C3×C4×C13 | C22 |
| hypercenter | C2×C4 | D3×D13 |
| hypocenter | C3×C13 | #120 |
| LCS | G ▷ C22×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C2×C4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×D3×D13 | C2 | semidirect |
| 2. C2×C3×D52 | C2 | semidirect |
| 3. C2×#64603 | C2 | semidirect |
| 4. C2×#64602 | C2 | semidirect |
| 5. #10597666 | C2 | semidirect |
| 6. C13×(C2×D3)⋊C4 | C2 | semidirect |
| 7. #10597608 | C2 | semidirect |
| 12. C22×C3×D13 | C22 | semidirect |
| 16. C2×C3×C4×C13 | C22 | semidirect |
| 17. C2×Dic39 | C22 | semidirect |
| 18. C2×Dic3×C13 | C22 | semidirect |
| 25. C2×D52 | D3 | semidirect |
| 32. C2×D39 | D4 | semidirect |
| 35. C2×D3×C13 | D4 | semidirect |
| 41. C2×C3×D13 | D4 | semidirect |
| 52. C22×D13 | C2×D3 | semidirect |
| 54. C2×C4×C13 | C2×D3 | semidirect |
| 80. C2×D13 | #67 | semidirect |
| 90. (C2×D3)⋊C4 | D13 | semidirect |
| 91. C3×C13 | #120 | semidirect |
| 108. C2×C3×C4 | C2×D13 | semidirect |
| 112. C2×Dic3 | C2×D13 | semidirect |
| 120. C13 | #937 | semidirect |
| 134. C2×D3 | D52 | semidirect |
| 150. C2×C4 | D3×D13 | semidirect |
| 175. C3 | #88136 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D3×D13 | 2 |
| C2×C3×D52 | 2 |
| C2×#64603 | 2 |
| C2×#64602 | 2 |
| #10597666 | 2 |
| C13×(C2×D3)⋊C4 | 2 |
| #10597608 | 2 |
| #88136 | 3 |
| #937 | 13 |