Finite Group DatabasebetaFinite Group DatabasebetaOrder 17792.
944 conjugacy classes of subgroups; only the 189 normal subgroups are shown.
This group has 944 conjugacy classes of subgroups — too many to draw. Only its 189 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D139 |
| commutator, socle, cosocle | C23×C139 | C24 |
| Frattini | C23 | C23×D139 |
| Fitting | C22×#41×C139 | C2 |
| hypercenter | C22×#41 | D139 |
| hypocenter | C139 | #2388 |
| LCS | G ▷ C23×C139 ▷ C139 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×C4×C22⋊D139 | C2 | semidirect |
| 2. #22580872 | C2 | semidirect |
| 3. #22580867 | C2 | semidirect |
| 4. #22580864 | C2 | semidirect |
| 5. #22580861 | C2 | semidirect |
| 6. C4×C22⋊Dic139 | C2 | semidirect |
| 7. C22×#41×C139 | C2 | semidirect |
| 41. C22×C4×C139 | D4 | semidirect |
| 46. C22×D139 | #41 | semidirect |
| 53. C2×Dic139 | #41 | semidirect |
| 88. C139 | #2388 | semidirect |
| 90. C22×#41 | D139 | semidirect |
| 125. C22×C4 | C22⋊D139 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×C22⋊D139 | 2 |
| #22580872 | 2 |
| #22580867 | 2 |
| #22580864 | 2 |
| #22580861 | 2 |
| C4×C22⋊Dic139 | 2 |
| C22×#41×C139 | 2 |
| #2388 | 139 |