Finite Group DatabasebetaFinite Group DatabasebetaOrder 22144.
296 conjugacy classes of subgroups; only the 156 normal subgroups are shown.
This group has 296 conjugacy classes of subgroups — too many to draw. Only its 156 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4×C173 | C22⋊C4 |
| commutator | C22 | C2×C42×C173 |
| Frattini, cosocle | C22×C4 | C23×C173 |
| socle | C22×C173 | C2×C22⋊C4 |
| prime radical | C23×C173 | C22×C4 |
| LCS | G ▷ C22 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C4×C173 ◁ C2×C42×C173 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 13. #101×C173 | C4 | direct (N × H) |
| 58. C4×C173 | #101 | direct (N × H) |
| 65. C173 | C4×#101 | direct (N × H) |
| 66. C4×#101 | C173 | direct (N × H) |
| 79. #101 | C4×C173 | direct (N × H) |
| 124. C4 | #101×C173 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×C4×Q8×C173 | 2 |
| C2×#101×C173 | 2 |
| C4×M16×C173 | 2 |
| #343×C173 | 2 |
| C4×#101 | 173 |