Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
568 conjugacy classes of subgroups; only the 114 normal subgroups are shown.
This group has 568 conjugacy classes of subgroups — too many to draw. Only its 114 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 | #469 |
| commutator, Frattini, cosocle | C22×C8 | C23×C7 |
| socle | C2×C7 | #1999 |
| LCS | G ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C4×C7 ◁ C22×C4×C7 ◁ C23×C7×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#3414 | C2 | semidirect |
| 2. C7×#3050 | C2 | semidirect |
| 3. C7×#2145 | C2 | semidirect |
| 4. C7×#2112 | C2 | semidirect |
| 5. C7×#1384 | C2 | semidirect |
| 21. #13309 | C7 | direct (N × H) |
| 28. C2×C7×Q16 | D4 | semidirect |
| 30. C2×C7×D8 | D4 | semidirect |
| 49. C2×C7×C16 | D4 | semidirect |
| 51. C7×#106 | D4 | semidirect |
| 54. #3414 | C2×C7 | semidirect |
| 55. #3050 | C2×C7 | semidirect |
| 56. #2145 | C2×C7 | semidirect |
| 57. #2112 | C2×C7 | semidirect |
| 58. #1384 | C2×C7 | semidirect |
| 148. C2×Q16 | C7×D4 | semidirect |
| 150. C2×D8 | C7×D4 | semidirect |
| 169. C2×C16 | C7×D4 | semidirect |
| 171. #106 | C7×D4 | semidirect |
| 263. C7 | #13309 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3414 | 2 |
| C7×#3050 | 2 |
| C7×#2145 | 2 |
| C7×#2112 | 2 |
| C7×#1384 | 2 |
| #13309 | 7 |