Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
276 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 276 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.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 5. C2×C4⋊#10624382 | C4 | semidirect |
| 9. (C2×#10624382)⋊C4 | C4 | semidirect |
| 12. C22⋊#13089678 | C4 | semidirect |
| 14. C22⋊C8×C181 | C4 | semidirect |
| 96. C181 | #1294 | semidirect |
| 108. C22⋊C8 | #10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26042221 | 2 |
| C2×(C2×#10624382)⋊C4 | 2 |
| C22⋊C8×D181 | 2 |
| #1294 | 181 |