Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
1034 conjugacy classes of subgroups; only the 130 normal subgroups are shown.
This group has 1034 conjugacy classes of subgroups — too many to draw. Only its 130 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C22×C7 | #386 |
| commutator | C22×C4 | C22×C4×C7 |
| Frattini, cosocle | C23×C4 | C23×C7 |
| prime radical | C7×#2433 | C2 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C23×C4×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2308 | C2 | semidirect |
| 3. C7×#1783 | C2 | semidirect |
| 4. C7×#1510 | C2 | semidirect |
| 5. C7×#1284 | C2 | semidirect |
| 7. C2×C7×#127 | C4 | semidirect |
| 15. C7×#390 | C4 | semidirect |
| 21. #9463 | C7 | direct (N × H) |
| 31. C22×C7×D4 | C2×C4 | semidirect |
| 41. C2×C7×C4⋊C4 | C2×C4 | semidirect |
| 51. C2×C42×C7 | C2×C4 | semidirect |
| 57. C7×#95 | D4 | semidirect |
| 59. #2308 | C2×C7 | semidirect |
| 60. #1783 | C2×C7 | semidirect |
| 61. #1510 | C2×C7 | semidirect |
| 62. #1284 | C2×C7 | semidirect |
| 122. C2×#127 | C4×C7 | semidirect |
| 130. #390 | C4×C7 | semidirect |
| 205. C22×D4 | C2×C4×C7 | semidirect |
| 215. C2×C4⋊C4 | C2×C4×C7 | semidirect |
| 225. C2×C42 | C2×C4×C7 | semidirect |
| 231. #95 | C7×D4 | semidirect |
| 395. C7 | #9463 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2433 | 2 |
| C7×#2308 | 2 |
| C7×#1783 | 2 |
| C7×#1510 | 2 |
| C7×#1284 | 2 |
| #9463 | 7 |