Finite Group DatabasebetaFinite Group DatabasebetaOrder 1792.
5142 conjugacy classes of subgroups; only the 907 normal subgroups are shown.
This group has 5142 conjugacy classes of subgroups — too many to draw. Only its 907 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×C7×#376 | C2 |
| socle | C24×C7 | C24 |
| hypercenter | C2×#376 | D7 |
| hypocenter | C7 | C2×#2657 |
| LCS | G ▷ C23×C7 ▷ C7 | |
| UCS | C1 ◁ C24 ◁ C2×#376 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×#6437 | C2 | semidirect |
| 2. C22×#6438 | C2 | semidirect |
| 3. C2×C7×#376 | C2 | semidirect |
| 4. #11730876 | C2 | direct (N × H) |
| 5. C2×#89443 | C2 | semidirect |
| 12. C2×#6438 | C22 | semidirect |
| 14. C2×#6437 | C22 | semidirect |
| 15. C7×#376 | C22 | semidirect |
| 17. #89443 | C22 | semidirect |
| 31. C2×C42×C7 | D4 | semidirect |
| 42. C2×#376 | D7 | semidirect |
| 63. C42×C7 | C2×D4 | semidirect |
| 75. #376 | C2×D7 | semidirect |
| 112. C2×C42 | D28 | semidirect |
| 147. C42 | C2×D28 | semidirect |
| 148. C2×C7 | #2657 | semidirect |
| 171. C7 | C2×#2657 | semidirect |
| 184. C2 | #11730876 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#6437 | 2 |
| C22×#6438 | 2 |
| C2×C7×#376 | 2 |
| #11730876 | 2 |
| C2×#89443 | 2 |
| C2×#2657 | 7 |