Finite Group DatabasebetaFinite Group DatabasebetaOrder 23168.
816 conjugacy classes of subgroups; only the 258 normal subgroups are shown.
This group has 816 conjugacy classes of subgroups — too many to draw. Only its 258 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. C2×#19153879 | C2 | direct (N × H) |
| 11. #19153879 | C22 | direct (N × H) |
| 13. C22×Dic362 | C4 | semidirect |
| 16. C2×Q8×D181 | C4 | semidirect |
| 20. C22×Q8×C181 | C4 | semidirect |
| 32. C2×Dic362 | C2×C4 | semidirect |
| 36. Q8×D181 | C2×C4 | semidirect |
| 47. C2×Q8×C181 | C2×C4 | semidirect |
| 60. Dic362 | C22×C4 | semidirect |
| 73. Q8×C181 | C22×C4 | semidirect |
| 77. C22×C181 | #103 | semidirect |
| 79. C2×D181 | #103 | semidirect |
| 91. C2×C181 | C2×#103 | semidirect |
| 93. D181 | C2×#103 | semidirect |
| 96. C181 | C22×#103 | semidirect |
| 108. C22×Q8 | #10624382 | semidirect |
| 129. C2×Q8 | C2×#10624382 | semidirect |
| 157. Q8 | C22×#10624382 | semidirect |
| 179. C22 | #19153879 | direct (N × H) |
| 191. C2 | C2×#19153879 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×D181⋊C8 | 2 |
| C22×C4⋊#10624382 | 2 |
| C2×#19153879 | 2 |
| C22×Q8×D181 | 2 |
| C22×#103 | 181 |