Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
3774 conjugacy classes of subgroups; only the 1579 normal subgroups are shown.
This group has 3774 conjugacy classes of subgroups — too many to draw. Only its 1579 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C24 | C23×D7 |
| commutator, cosocle | C23×C7 | C25 |
| Frattini | C23 | C24×D7 |
| Fitting | C2×C43×C7 | C2 |
| socle, prime radical | C24×C7 | C24 |
| hypercenter | C2×C43 | D7 |
| hypocenter | C7 | C2×#2868 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×C43 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 4. #11730756 | C2 | direct (N × H) |
| 20. C2×C42×C7 | Q8 | semidirect |
| 41. C42×C7 | C2×Q8 | semidirect |
| 55. C2×C4×C7 | C4⋊Q8 | semidirect |
| 70. C2×C42 | Dic14 | semidirect |
| 79. C4×C7 | C2×C4⋊Q8 | semidirect |
| 92. C42 | C2×Dic14 | semidirect |
| 94. C2×C7 | #2868 | semidirect |
| 103. C2×C4 | #6432 | semidirect |
| 108. C7 | C2×#2868 | semidirect |
| 114. C4 | C2×#6432 | semidirect |
| 116. C2 | #11730756 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6432 | 2 |
| C2×C43×C7 | 2 |
| C2×#89707 | 2 |
| #11730756 | 2 |
| C2×#2868 | 7 |