Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
128 conjugacy classes of subgroups; only the 43 normal subgroups are shown.
This group has 128 conjugacy classes of subgroups — too many to draw. Only its 43 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×C7×SD16 | C2 | semidirect |
| 2. Q8×Dic7 | C2 | semidirect |
| 3. C2×#1143 | C2 | semidirect |
| 5. #6406 | C2 | semidirect |
| 6. #6395 | C2 | semidirect |
| 7. Dic7⋊C8 | C2 | semidirect |
| 25. C7×Q8 | D4 | semidirect |
| 40. C2×SD16 | D7 | semidirect |
| 58. Dic7 | SD16 | semidirect |
| 80. Q8 | C22⋊D7 | semidirect |
| 94. C7 | #460 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×SD16 | 2 |
| Q8×Dic7 | 2 |
| C2×#1143 | 2 |
| #6503 | 2 |
| #6406 | 2 |
| #6395 | 2 |
| Dic7⋊C8 | 2 |
| #460 | 7 |