Finite Group DatabasebetaFinite Group DatabasebetaOrder 896.
552 conjugacy classes of subgroups; only the 181 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 181 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 |
|---|---|---|
| 5. #89953 | C2 | direct (N × H) |
| 63. C2×Dic7 | Q16 | semidirect |
| 93. Dic7 | C2×Q16 | semidirect |
| 116. C2×C7 | #494 | semidirect |
| 138. C7 | C2×#494 | semidirect |
| 148. C2 | #89953 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×Q16 | 2 |
| C2×#6507 | 2 |
| C22×#1144 | 2 |
| C22×Dic28 | 2 |
| #89953 | 2 |
| C2×C8×Dic7 | 2 |
| C2×#494 | 7 |