Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
248 conjugacy classes of subgroups; only the 80 normal subgroups are shown.
This group has 248 conjugacy classes of subgroups — too many to draw. Only its 80 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C8×D21 | C2 | semidirect |
| 2. C2×C3×#1131 | C2 | semidirect |
| 4. C7×#815 | C2 | semidirect |
| 5. Dic3⋊(C7⋊C8) | C2 | semidirect |
| 6. #10620492 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 22. C2×#1131 | D3 | semidirect |
| 42. C3×C7×C8 | D4 | semidirect |
| 64. #815 | D7 | semidirect |
| 69. C2×D21 | M16 | semidirect |
| 93. C7×C8 | #67 | semidirect |
| 147. C3×C8 | D28 | semidirect |
| 150. C3×C7 | #435 | semidirect |
| 197. C8 | #4246 | semidirect |
| 198. C7 | #5127 | semidirect |
| 217. C3 | #89478 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C8×D21 | 2 |
| C2×C3×#1131 | 2 |
| C4×#4246 | 2 |
| C7×#815 | 2 |
| Dic3⋊(C7⋊C8) | 2 |
| #10620492 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89478 | 3 |
| #5127 | 7 |