Finite Group DatabasebetaFinite Group DatabasebetaOrder 448.
122 conjugacy classes of subgroups; only the 53 normal subgroups are shown.
This group has 122 conjugacy classes of subgroups — too many to draw. Only its 53 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×M16 | C2 | semidirect |
| 3. C2×#1131 | C2 | semidirect |
| 4. C22⋊(C7⋊C8) | C2 | semidirect |
| 5. (C2×D7)⋊C8 | C2 | semidirect |
| 6. Dic7⋊C8 | C2 | semidirect |
| 7. C8×Dic7 | C2 | semidirect |
| 35. C7×C8 | D4 | semidirect |
| 39. C2×M16 | D7 | semidirect |
| 57. Dic7 | M16 | semidirect |
| 91. C8 | C22⋊D7 | semidirect |
| 92. C7 | #436 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C7×M16 | 2 |
| C4×C22⋊D7 | 2 |
| C2×#1131 | 2 |
| C22⋊(C7⋊C8) | 2 |
| (C2×D7)⋊C8 | 2 |
| Dic7⋊C8 | 2 |
| C8×Dic7 | 2 |
| #436 | 7 |