Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 76 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 76 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×Q8×D7 | C2 | semidirect |
| 2. C2×C7×#215 | C2 | semidirect |
| 4. C2×#66564 | C2 | semidirect |
| 5. #10620674 | C2 | semidirect |
| 6. #10620506 | C2 | semidirect |
| 7. (C2×D7)⋊(C3⋊C8) | C2 | semidirect |
| 24. C2×Q8×D7 | D3 | semidirect |
| 35. C3×C7×Q8 | D4 | semidirect |
| 48. C3×Dic14 | D4 | semidirect |
| 69. C2×#215 | D7 | semidirect |
| 80. C2×C3×D7 | SD16 | semidirect |
| 91. C7×Q8 | #67 | semidirect |
| 105. Dic14 | #67 | semidirect |
| 141. C2×D7 | #215 | semidirect |
| 154. C3×Q8 | C22⋊D7 | semidirect |
| 168. C3×C7 | #448 | semidirect |
| 208. Q8 | #4245 | semidirect |
| 222. C7 | #5227 | semidirect |
| 241. C3 | #89942 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C3×Q8×D7 | 2 |
| C2×C7×#215 | 2 |
| #10621011 | 2 |
| C2×#66564 | 2 |
| #10620674 | 2 |
| #10620506 | 2 |
| (C2×D7)⋊(C3⋊C8) | 2 |
| #89942 | 3 |
| #5227 | 7 |