Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
6146 conjugacy classes of subgroups; only the 494 normal subgroups are shown.
This group has 6146 conjugacy classes of subgroups — too many to draw. Only its 494 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C24×C7 | C24 |
| commutator, Frattini, cosocle | C24 | C24×C7 |
| LCS | G ▷ C24 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C7×#120 | C2 | semidirect |
| 2. C7×#1438 | C2 | semidirect |
| 3. C26×C7 | C22 | semidirect |
| 6. C22×C7×C22⋊C4 | C22 | semidirect |
| 7. C2×C7×#95 | C22 | semidirect |
| 8. #15947 | C7 | direct (N × H) |
| 14. C22×C7×D4 | D4 | semidirect |
| 20. C22×#120 | C2×C7 | semidirect |
| 21. #1438 | C2×C7 | semidirect |
| 38. C26 | C22×C7 | semidirect |
| 41. C22×C22⋊C4 | C22×C7 | semidirect |
| 42. C2×#95 | C22×C7 | semidirect |
| 52. C23×C7 | #120 | semidirect |
| 64. C22×D4 | C7×D4 | semidirect |
| 107. C23 | C7×#120 | semidirect |
| 114. C7 | #15947 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×#120 | 2 |
| C7×#1438 | 2 |
| #15947 | 7 |