Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
332 conjugacy classes of subgroups; only the 66 normal subgroups are shown.
This group has 332 conjugacy classes of subgroups — too many to draw. Only its 66 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 |
|---|---|---|
| 1. #41×#10624382 | C2 | semidirect |
| 2. #26042276 | C2 | semidirect |
| 3. C2×#19153881 | C2 | semidirect |
| 4. #26042260 | C2 | semidirect |
| 5. #26042162 | C2 | semidirect |
| 6. #26042151 | C2 | semidirect |
| 25. #19153847 | C4 | semidirect |
| 26. #19153844 | C4 | semidirect |
| 28. #19153841 | C4 | semidirect |
| 32. #137×C181 | C4 | semidirect |
| 61. C2×D724 | C2×C4 | semidirect |
| 73. #15668433 | C2×C4 | semidirect |
| 77. C2×Q8×C181 | C2×C4 | semidirect |
| 80. M16×C181 | C2×C4 | semidirect |
| 150. C181 | #1906 | semidirect |
| 163. #137 | #10624382 | semidirect |
| 195. C2×Q8 | C2×#10624382 | semidirect |
| 217. M16 | 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 |
| #26042276 | 2 |
| C2×#19153881 | 2 |
| #26042260 | 2 |
| #26042162 | 2 |
| #26042151 | 2 |
| #26042078 | 2 |
| #1906 | 181 |