Finite Group DatabasebetaFinite Group DatabasebetaOrder 1344.
316 conjugacy classes of subgroups; only the 96 normal subgroups are shown.
This group has 316 conjugacy classes of subgroups — too many to draw. Only its 96 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 |
|---|---|---|
| 2. C2×#1131⋊C3 | C2 | semidirect |
| 3. C2×C8×AGL(1,𝔽7) | C2 | semidirect |
| 4. ΓL(1,𝔽8)×C22⋊C8 | C2 | semidirect |
| 5. (C22⋊(C7⋊C8))⋊C3 | C2 | semidirect |
| 6. (C2×AGL(1,𝔽7))⋊C8 | C2 | semidirect |
| 7. (C2×AGL(1,𝔽7))⋊C8 | C2 | semidirect |
| 8. #89499 | C3 | semidirect |
| 25. C2×#1131 | C2×C3 | semidirect |
| 26. C2×C8×D7 | C2×C3 | semidirect |
| 27. C7×C22⋊C8 | C2×C3 | semidirect |
| 28. C22⋊(C7⋊C8) | C2×C3 | semidirect |
| 29. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 30. (C2×D7)⋊C8 | C2×C3 | semidirect |
| 139. C22⋊C8 | AGL(1,𝔽7) | semidirect |
| 176. ΓL(1,𝔽8) | #408 | semidirect |
| 234. C7 | C3×#408 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#1157⋊C3 | 2 |
| C2×#1131⋊C3 | 2 |
| C2×C8×AGL(1,𝔽7) | 2 |
| ΓL(1,𝔽8)×C22⋊C8 | 2 |
| (C22⋊(C7⋊C8))⋊C3 | 2 |
| (C2×AGL(1,𝔽7))⋊C8 | 2 |
| #89499 | 3 |
| C3×#408 | 7 |