Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
380 conjugacy classes of subgroups; only the 144 normal subgroups are shown.
This group has 380 conjugacy classes of subgroups — too many to draw. Only its 144 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C23×C173 | C2×D4 |
| commutator | C2×C4 | C22×C4×C173 |
| Frattini, cosocle | C22×C4 | C23×C173 |
| prime radical | C24×C173 | D4 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C23×C173 ◁ C23×C4×C173 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. C2×#103×C173 | C2 | semidirect |
| 5. #340×C173 | C2 | semidirect |
| 12. C22⋊Q8×C173 | C4 | semidirect |
| 75. C22×C173 | #103 | semidirect |
| 94. C173 | #1892 | direct (N × H) |
| 95. #1892 | C173 | direct (N × H) |
| 98. C2×#103 | C2×C173 | semidirect |
| 100. #340 | C2×C173 | semidirect |
| 107. C22⋊Q8 | C4×C173 | semidirect |
| 170. C22 | #103×C173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C23×C8×C173 | 2 |
| C2×C22⋊Q8×C173 | 2 |
| C2×#103×C173 | 2 |
| #380×C173 | 2 |
| #340×C173 | 2 |
| #1892 | 173 |