Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
132 conjugacy classes of subgroups; only the 49 normal subgroups are shown.
This group has 132 conjugacy classes of subgroups — too many to draw. Only its 49 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. D4×Dic7 | C2 | semidirect |
| 3. #6456 | C2 | semidirect |
| 4. C7×#102 | C2 | semidirect |
| 5. #6395 | C2 | semidirect |
| 6. #6389 | C2 | semidirect |
| 7. #6382 | C2 | semidirect |
| 15. #1141 | C4 | semidirect |
| 24. C7×D4 | C2×C4 | semidirect |
| 32. D28 | C2×C4 | semidirect |
| 35. C7⋊C8 | C2×C4 | semidirect |
| 41. #102 | D7 | semidirect |
| 78. D4 | C4×D7 | semidirect |
| 88. C7 | #442 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| D4×Dic7 | 2 |
| C2×#1141 | 2 |
| #6456 | 2 |
| C7×#102 | 2 |
| #6395 | 2 |
| #6389 | 2 |
| #6382 | 2 |
| #442 | 7 |