Finite Group DatabasebetaFinite Group DatabasebetaOrder 1248.
328 conjugacy classes of subgroups; only the 127 normal subgroups are shown.
This group has 328 conjugacy classes of subgroups — too many to draw. Only its 127 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22 | C22×D39 |
| commutator, cosocle | C2×C3×C13 | C24 |
| Frattini | C2 | C23×D39 |
| Fitting | C2×C3×D4×C13 | C2 |
| socle | C22×C3×C13 | C23 |
| hypercenter | C2×D4 | D39 |
| hypocenter | C3×C13 | C2×#41 |
| LCS | G ▷ C2×C3×C13 ▷ C3×C13 | |
| UCS | C1 ◁ C22 ◁ C2×D4 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C3×D4×C13 | C2 | semidirect |
| 2. C2×#64625 | C2 | semidirect |
| 3. C22×Dic39 | C2 | semidirect |
| 4. #10597792 | C2 | direct (N × H) |
| 5. C2×C4×D39 | C2 | semidirect |
| 6. C2×Dic78 | C2 | semidirect |
| 10. C3×D4×C13 | C22 | semidirect |
| 12. #64625 | C22 | semidirect |
| 15. C2×Dic39 | C22 | semidirect |
| 16. C4×D39 | C22 | semidirect |
| 17. Dic78 | C22 | semidirect |
| 18. C2×D4×C13 | D3 | semidirect |
| 34. D4×C13 | C2×D3 | semidirect |
| 44. C2×C3×C13 | #41 | semidirect |
| 55. C2×C3×D4 | D13 | semidirect |
| 61. C3×C13 | C2×#41 | semidirect |
| 64. C2×C13 | #237 | semidirect |
| 69. C3×D4 | C2×D13 | semidirect |
| 80. C2×D4 | D39 | semidirect |
| 83. C13 | C2×#237 | semidirect |
| 96. D4 | C2×D39 | semidirect |
| 103. C2×C3 | #6129 | semidirect |
| 114. C3 | C2×#6129 | semidirect |
| 117. C2 | #10597792 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×D4×C13 | 2 |
| C2×#64625 | 2 |
| C22×Dic39 | 2 |
| #10597792 | 2 |
| C2×C4×D39 | 2 |
| C2×Dic78 | 2 |
| C2×#6129 | 3 |
| C2×#237 | 13 |