Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
692 conjugacy classes of subgroups; only the 253 normal subgroups are shown.
This group has 692 conjugacy classes of subgroups — too many to draw. Only its 253 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 3. #26041210 | C2 | direct (N × H) |
| 81. C2×C181 | #398 | semidirect |
| 87. C181 | C2×#398 | semidirect |
| 169. C2 | #26041210 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#15668428 | 2 |
| #26041210 | 2 |
| C2×#19153723 | 2 |
| C22×C4⋊C4×C181 | 2 |
| C2×#398 | 181 |