Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
524 conjugacy classes of subgroups; only the 153 normal subgroups are shown.
This group has 524 conjugacy classes of subgroups — too many to draw. Only its 153 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 | C23×D139 |
| commutator, socle, cosocle | C23×C139 | C24 |
| Fitting | #390×C139 | C2 |
| prime radical | C22×D4×C139 | C22 |
| hypercenter | #390 | D139 |
| hypocenter | C139 | #2861 |
| LCS | G ▷ C23×C139 ▷ C139 | |
| UCS | C1 ◁ C23 ◁ #390 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#17984833 | C2 | semidirect |
| 3. #22580859 | C2 | semidirect |
| 4. #22580858 | C2 | semidirect |
| 6. #22580846 | C2 | semidirect |
| 7. #22580841 | C2 | semidirect |
| 8. C42×Dic139 | C2 | semidirect |
| 109. C139 | #2861 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#17984833 | 2 |
| C2×#17984829 | 2 |
| #22580859 | 2 |
| #22580858 | 2 |
| #22580856 | 2 |
| #22580846 | 2 |
| #22580841 | 2 |
| C42×Dic139 | 2 |
| #390×C139 | 2 |
| #2861 | 139 |