Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
4086 conjugacy classes of subgroups; only the 811 normal subgroups are shown.
This group has 4086 conjugacy classes of subgroups — too many to draw. Only its 811 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C23 | C24×D7 |
| commutator, socle, cosocle | C23×C7 | C25 |
| Fitting | C7×#2867 | C2 |
| hypercenter | #2867 | D7 |
| hypocenter | C7 | #36644 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C23 ◁ #2867 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#90407 | C2 | semidirect |
| 2. C7×#2867 | C2 | semidirect |
| 3. #11740637 | C2 | semidirect |
| 4. #11740629 | C2 | semidirect |
| 5. Dic7×#127 | C2 | semidirect |
| 6. C43×D7 | C2 | semidirect |
| 7. #11730756 | C2 | semidirect |
| 45. C42×D7 | D4 | semidirect |
| 49. #2867 | D7 | semidirect |
| 72. C42×C7 | #41 | semidirect |
| 110. C4×D7 | #127 | semidirect |
| 142. C4×C7 | #532 | semidirect |
| 169. C42 | #1159 | semidirect |
| 193. C7 | #36644 | semidirect |
| 204. C4 | #90407 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#90407 | 2 |
| C7×#2867 | 2 |
| #11740637 | 2 |
| #11740629 | 2 |
| Dic7×#127 | 2 |
| C43×D7 | 2 |
| #11730756 | 2 |
| #36644 | 7 |