Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
376 conjugacy classes of subgroups; only the 70 normal subgroups are shown.
This group has 376 conjugacy classes of subgroups — too many to draw. Only its 70 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 | #1613 |
| commutator, Frattini, cosocle | C2×M16 | C23×C7 |
| prime radical | C7×#3192 | C2 |
| LCS | G ▷ C2×M16 ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C7 ◁ C2×C4×C7 ◁ C2×C7×M16 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2238 | C2 | semidirect |
| 3. C7×#2091 | C2 | semidirect |
| 4. C7×#1341 | C2 | semidirect |
| 5. C7×#1320 | C2 | semidirect |
| 12. C7×#430 | C22 | semidirect |
| 17. C7×#349 | C22 | semidirect |
| 18. C7×#338 | C22 | semidirect |
| 19. #12298 | C7 | direct (N × H) |
| 45. #2238 | C2×C7 | semidirect |
| 46. #2091 | C2×C7 | semidirect |
| 47. #1341 | C2×C7 | semidirect |
| 48. #1320 | C2×C7 | semidirect |
| 88. #430 | C22×C7 | semidirect |
| 93. #349 | C22×C7 | semidirect |
| 94. #338 | C22×C7 | semidirect |
| 230. C7 | #12298 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#3192 | 2 |
| C7×#2238 | 2 |
| C7×#2091 | 2 |
| C7×#1341 | 2 |
| C7×#1320 | 2 |
| #12298 | 7 |