Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
332 conjugacy classes of subgroups; only the 106 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 106 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 |
|---|---|---|
| 10. Q8×#10624382 | C4 | semidirect |
| 17. #19153879 | C4 | semidirect |
| 23. #19153741 | C4 | semidirect |
| 24. #19153740 | C4 | semidirect |
| 25. #19153739 | C4 | semidirect |
| 26. #103×C181 | C4 | semidirect |
| 77. Dic362 | C42 | semidirect |
| 91. Q8×C181 | C42 | semidirect |
| 106. #10624382 | #103 | direct (N × H) |
| 122. C181 | C4×#103 | semidirect |
| 147. #103 | #10624382 | direct (N × H) |
| 189. Q8 | C4×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10624382 | 2 |
| C2×#19153879 | 2 |
| C2×C8×#10624382 | 2 |
| C4⋊C4×#10624382 | 2 |
| #26042153 | 2 |
| #26042152 | 2 |
| #103×D181 | 2 |
| C4×#103 | 181 |