Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
444 conjugacy classes of subgroups; only the 95 normal subgroups are shown.
This group has 444 conjugacy classes of subgroups — too many to draw. Only its 95 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. C22×#1142 | C2 | semidirect |
| 3. C2×#6487 | C2 | semidirect |
| 4. C2×#6406 | C2 | semidirect |
| 5. C2×C22⋊(C7⋊C8) | C2 | semidirect |
| 6. C2×#6384 | C2 | semidirect |
| 7. #89324 | C2 | semidirect |
| 57. C2×Dic14 | D4 | semidirect |
| 64. C4⋊Dic7 | D4 | semidirect |
| 71. C2×C7⋊C8 | D4 | semidirect |
| 92. C23×C7 | SD16 | semidirect |
| 241. C23 | #1142 | semidirect |
| 276. C7 | #2000 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×#121 | 2 |
| C22×#1142 | 2 |
| C2×#6487 | 2 |
| C2×#6406 | 2 |
| C2×C22⋊(C7⋊C8) | 2 |
| C2×#6384 | 2 |
| #89324 | 2 |
| #2000 | 7 |