Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
908 conjugacy classes of subgroups; only the 250 normal subgroups are shown.
This group has 908 conjugacy classes of subgroups — too many to draw. Only its 250 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C4×C7 | C2×#127 |
| commutator, Frattini, cosocle | C22×C4 | C24×C7 |
| socle | C2×C7 | #2397 |
| LCS | G ▷ C22×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2955 | C2 | semidirect |
| 2. C7×#2930 | C2 | semidirect |
| 3. C7×#2098 | C2 | semidirect |
| 4. C7×#2091 | C2 | semidirect |
| 5. C7×#2017 | C2 | semidirect |
| 6. C7×#2010 | C2 | semidirect |
| 7. C7×#1747 | C2 | semidirect |
| 24. #23795 | C7 | direct (N × H) |
| 51. C7×#97 | D4 | semidirect |
| 52. C4×C7×C8 | D4 | semidirect |
| 53. #2955 | C2×C7 | semidirect |
| 54. #2930 | C2×C7 | semidirect |
| 55. #2098 | C2×C7 | semidirect |
| 56. #2091 | C2×C7 | semidirect |
| 57. #2017 | C2×C7 | semidirect |
| 58. #2010 | C2×C7 | semidirect |
| 59. #1747 | C2×C7 | semidirect |
| 157. #97 | C7×D4 | semidirect |
| 158. C4×C8 | C7×D4 | semidirect |
| 230. C7 | #23795 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2955 | 2 |
| C7×#2930 | 2 |
| C7×#2098 | 2 |
| C7×#2091 | 2 |
| C7×#2017 | 2 |
| C7×#2010 | 2 |
| C7×#1747 | 2 |
| #23795 | 7 |