Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
320 conjugacy classes of subgroups; only the 88 normal subgroups are shown.
This group has 320 conjugacy classes of subgroups — too many to draw. Only its 88 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. M16×#10624382 | C2 | semidirect |
| 4. #26042215 | C2 | semidirect |
| 5. #26042151 | C2 | semidirect |
| 6. #26042150 | C2 | semidirect |
| 9. Q8×#10624382 | C4 | semidirect |
| 11. D4×#10624382 | C4 | semidirect |
| 17. #19153881 | C4 | semidirect |
| 18. #19153880 | C4 | semidirect |
| 25. #19153744 | C4 | semidirect |
| 26. #19153743 | C4 | semidirect |
| 27. #19153742 | C4 | semidirect |
| 28. #104×C181 | C4 | semidirect |
| 32. #15668459 | C2×C4 | semidirect |
| 43. C4×#10624382 | C2×C4 | semidirect |
| 57. #15668433 | C2×C4 | semidirect |
| 61. C4×Dic181 | C2×C4 | semidirect |
| 63. M16×C181 | C2×C4 | semidirect |
| 64. C42×C181 | C2×C4 | semidirect |
| 126. C181 | #1759 | semidirect |
| 152. #104 | #10624382 | semidirect |
| 175. M16 | C2×#10624382 | semidirect |
| 191. C42 | C2×#10624382 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #41×#10624382 | 2 |
| D181⋊#104 | 2 |
| M16×#10624382 | 2 |
| #26042215 | 2 |
| #26042151 | 2 |
| #26042150 | 2 |
| #104×D181 | 2 |
| #1759 | 181 |