Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
120 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 120 conjugacy classes of subgroups — too many to draw. Only its 60 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 | #476 |
| commutator, Frattini, cosocle | C2×C8 | C23×C173 |
| prime radical | #135×C173 | C22 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C173 ◁ C2×C4×C173 ◁ C4×C8×C173 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #499×C173 | C2 | semidirect |
| 3. #365×C173 | C2 | semidirect |
| 4. #364×C173 | C2 | semidirect |
| 50. C173 | #2231 | direct (N × H) |
| 51. #2231 | C173 | direct (N × H) |
| 52. #499 | C2×C173 | semidirect |
| 54. #365 | C2×C173 | semidirect |
| 55. #364 | C2×C173 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #499×C173 | 2 |
| #443×C173 | 2 |
| #365×C173 | 2 |
| #364×C173 | 2 |
| #360×C173 | 2 |
| #2231 | 173 |