Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
496 conjugacy classes of subgroups; only the 118 normal subgroups are shown.
This group has 496 conjugacy classes of subgroups — too many to draw. Only its 118 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 | C2×C42 | C23×C7 |
| prime radical | C7×#392 | C4 |
| LCS | G ▷ C22×C4 ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C7 ◁ C2×C42×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C7×#2921 | C2 | semidirect |
| 3. C7×#1527 | C2 | semidirect |
| 4. C7×#1464 | C2 | semidirect |
| 5. C7×#1300 | C2 | semidirect |
| 25. #9389 | C7 | direct (N × H) |
| 54. C7×#97 | D4 | semidirect |
| 61. #2921 | C2×C7 | semidirect |
| 63. #1527 | C2×C7 | semidirect |
| 64. #1464 | C2×C7 | semidirect |
| 65. #1300 | C2×C7 | semidirect |
| 200. #97 | C7×D4 | semidirect |
| 328. C7 | #9389 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C7×#2921 | 2 |
| C7×#2610 | 2 |
| C7×#1527 | 2 |
| C7×#1464 | 2 |
| C7×#1300 | 2 |
| #9389 | 7 |