Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
312 conjugacy classes of subgroups; only the 108 normal subgroups are shown.
This group has 312 conjugacy classes of subgroups — too many to draw. Only its 108 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C173 | #386 |
| commutator | C2×C4 | C22×C4×C173 |
| Frattini, cosocle | C22×C4 | C23×C173 |
| prime radical | C2×#41×C173 | C22 |
| LCS | G ▷ C2×C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C173 ◁ C22×C4×C173 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #419×C173 | C2 | semidirect |
| 5. H(3,ℤ/4)×C173 | C2 | semidirect |
| 11. C4⋊Q8×C173 | C4 | semidirect |
| 12. #124×C173 | C4 | semidirect |
| 80. C173 | #1909 | direct (N × H) |
| 81. #1909 | C173 | direct (N × H) |
| 84. #419 | C2×C173 | semidirect |
| 86. H(3,ℤ/4) | C2×C173 | semidirect |
| 92. C4⋊Q8 | C4×C173 | semidirect |
| 93. #124 | C4×C173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #568×C173 | 2 |
| #536×C173 | 2 |
| #419×C173 | 2 |
| #410×C173 | 2 |
| H(3,ℤ/4)×C173 | 2 |
| #1909 | 173 |