Finite Group DatabasebetaFinite Group DatabasebetaOrder 11072.
292 conjugacy classes of subgroups; only the 113 normal subgroups are shown.
This group has 292 conjugacy classes of subgroups — too many to draw. Only its 113 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C22 | C23×D173 |
| commutator, socle, cosocle | C22×C173 | C24 |
| Fitting | C2×#41×C173 | C2 |
| hypercenter | C2×#41 | D173 |
| hypocenter | C173 | #547 |
| LCS | G ▷ C22×C173 ▷ C173 | |
| UCS | C1 ◁ C22 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#14583825 | C2 | semidirect |
| 2. #19149677 | C2 | semidirect |
| 3. #19149662 | C2 | semidirect |
| 4. #19149660 | C2 | semidirect |
| 5. #19149658 | C2 | semidirect |
| 6. #19149655 | C2 | semidirect |
| 7. #19149651 | C2 | semidirect |
| 8. D4×Dic173 | C2 | semidirect |
| 9. C4×C22⋊D173 | C2 | semidirect |
| 10. C2×#14583805 | C2 | semidirect |
| 11. C2×#41×C173 | C2 | semidirect |
| 53. D4×C173 | D4 | semidirect |
| 76. Dic173 | #41 | semidirect |
| 83. C173 | #547 | semidirect |
| 86. C2×#41 | D173 | semidirect |
| 129. D4 | C22⋊D173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#14583825 | 2 |
| #19149677 | 2 |
| #19149662 | 2 |
| #19149660 | 2 |
| #19149658 | 2 |
| #19149655 | 2 |
| #19149651 | 2 |
| D4×Dic173 | 2 |
| C4×C22⋊D173 | 2 |
| C2×#14583805 | 2 |
| C2×#41×C173 | 2 |
| #547 | 173 |