Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1672 conjugacy classes of subgroups; only the 282 normal subgroups are shown.
This group has 1672 conjugacy classes of subgroups — too many to draw. Only its 282 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C7 | #2403 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C22×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3486 | C2 | semidirect |
| 2. C7×#3020 | C2 | semidirect |
| 3. C7×#2010 | C2 | semidirect |
| 4. C7×#1912 | C2 | semidirect |
| 5. C7×#1784 | C2 | semidirect |
| 22. #23899 | C7 | direct (N × H) |
| 40. C7×C4⋊Q8 | D4 | semidirect |
| 42. C7×#124 | D4 | semidirect |
| 60. #3486 | C2×C7 | semidirect |
| 61. #3020 | C2×C7 | semidirect |
| 62. #2010 | C2×C7 | semidirect |
| 63. #1912 | C2×C7 | semidirect |
| 64. #1784 | C2×C7 | semidirect |
| 169. C4⋊Q8 | C7×D4 | semidirect |
| 171. #124 | C7×D4 | semidirect |
| 280. C7 | #23899 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3486 | 2 |
| C7×#3020 | 2 |
| C7×#2010 | 2 |
| C7×#1912 | 2 |
| C7×#1784 | 2 |
| #23899 | 7 |