Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
154 conjugacy classes of subgroups; only the 27 normal subgroups are shown.
This group has 154 conjugacy classes of subgroups — too many to draw. Only its 27 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. C7×Q8×A4 | C2 | semidirect |
| 3. C7⋊(A4⋊C8) | C2 | semidirect |
| 9. C22×C7×Q8 | D3 | semidirect |
| 36. Q8×A4 | D7 | semidirect |
| 40. C7×A4 | SD16 | semidirect |
| 49. C7×Q8 | S4 | semidirect |
| 67. C22×Q8 | D21 | semidirect |
| 76. C22×C7 | #215 | semidirect |
| 110. A4 | #1143 | semidirect |
| 118. Q8 | C7⋊S4 | semidirect |
| 130. C7 | #5417 | semidirect |
| 138. C22 | #66634 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×Q8×A4 | 2 |
| C4⋊(C7⋊S4) | 2 |
| C7⋊(A4⋊C8) | 2 |
| #89999 | 3 |
| #66634 | 4 |
| #5417 | 7 |