Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
624 conjugacy classes of subgroups; only the 226 normal subgroups are shown.
This group has 624 conjugacy classes of subgroups — too many to draw. Only its 226 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×C3×C7×#41 | C2 | semidirect |
| 2. C2×C7×#239 | C2 | semidirect |
| 3. C7×Q8×Dic3 | C2 | semidirect |
| 4. C7×#940 | C2 | semidirect |
| 5. C7×#938 | C2 | semidirect |
| 6. C7×#930 | C2 | semidirect |
| 7. C4×C7×#67 | C2 | semidirect |
| 24. C2×C7×#41 | D3 | semidirect |
| 30. #5834 | C7 | direct (N × H) |
| 33. C3×C7×Q8 | D4 | semidirect |
| 59. C2×C3×#41 | C2×C7 | semidirect |
| 60. C2×#239 | C2×C7 | semidirect |
| 61. Q8×Dic3 | C2×C7 | semidirect |
| 62. #940 | C2×C7 | semidirect |
| 63. #938 | C2×C7 | semidirect |
| 64. #930 | C2×C7 | semidirect |
| 65. C4×#67 | C2×C7 | semidirect |
| 77. C7×Dic3 | #41 | semidirect |
| 81. C7×Q8 | #67 | semidirect |
| 113. C2×#41 | D3×C7 | semidirect |
| 133. C3×Q8 | C7×D4 | semidirect |
| 145. C3×C7 | #550 | semidirect |
| 176. Dic3 | C7×#41 | semidirect |
| 179. Q8 | C7×#67 | semidirect |
| 191. C7 | #5834 | direct (N × H) |
| 209. C3 | C7×#550 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×C7×#41 | 2 |
| C2×C7×#239 | 2 |
| C7×Q8×Dic3 | 2 |
| C7×#940 | 2 |
| C7×#938 | 2 |
| C7×#930 | 2 |
| C4×C7×#67 | 2 |
| C7×#550 | 3 |
| #5834 | 7 |