Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3774 conjugacy classes of subgroups; only the 1886 normal subgroups are shown.
This group has 3774 conjugacy classes of subgroups — too many to draw. Only its 1886 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle, prime radical | C24×C7 | C24 |
| commutator, Frattini, cosocle | C23 | C25×C7 |
| LCS | G ▷ C23 ▷ C1 | |
| UCS | C1 ◁ C24×C7 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. C7×#2868 | C2 | direct (N × H) |
| 13. C2×#2868 | C7 | direct (N × H) |
| 23. C2×C42×C7 | Q8 | semidirect |
| 27. #2868 | C2×C7 | direct (N × H) |
| 42. C42×C7 | C2×Q8 | semidirect |
| 58. C2×C4×C7 | C4⋊Q8 | semidirect |
| 71. C2×C42 | C7×Q8 | semidirect |
| 80. C4×C7 | C2×C4⋊Q8 | semidirect |
| 93. C42 | C2×C7×Q8 | semidirect |
| 94. C2×C7 | #2868 | direct (N × H) |
| 104. C2×C4 | C7×C4⋊Q8 | semidirect |
| 108. C7 | C2×#2868 | direct (N × H) |
| 115. C4 | C2×C7×C4⋊Q8 | semidirect |
| 116. C2 | C7×#2868 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C7×C4⋊Q8 | 2 |
| C7×#2868 | 2 |
| C2×C7×#384 | 2 |
| C2×C43×C7 | 2 |
| C2×#2868 | 7 |