Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
552 conjugacy classes of subgroups; only the 205 normal subgroups are shown.
This group has 552 conjugacy classes of subgroups — too many to draw. Only its 205 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 |
|---|---|---|
| 2. C2×#18011876 | C2 | semidirect |
| 4. #23749712 | C2 | direct (N × H) |
| 5. C2×#18011834 | C2 | semidirect |
| 7. C2×C8×Dic149 | C2 | semidirect |
| 8. C2×#106×C149 | C2 | semidirect |
| 12. C2×#14558725 | C4 | semidirect |
| 16. #18011876 | C22 | semidirect |
| 23. #18011834 | C22 | semidirect |
| 25. C8×Dic149 | C22 | semidirect |
| 29. #106×C149 | C22 | semidirect |
| 33. C2×Dic298 | C2×C4 | semidirect |
| 44. #14558725 | C2×C4 | semidirect |
| 55. C2×C8×C149 | C2×C4 | semidirect |
| 67. Dic298 | C22×C4 | semidirect |
| 74. C2×Dic149 | SD16 | semidirect |
| 88. C8×C149 | C22×C4 | semidirect |
| 104. Dic149 | C2×SD16 | semidirect |
| 105. C2×C149 | C4×SD16 | semidirect |
| 110. C149 | C2×C4×SD16 | semidirect |
| 116. C2×#106 | D149 | semidirect |
| 137. #106 | C2×D149 | semidirect |
| 161. C2×C8 | C4×D149 | semidirect |
| 199. C8 | C2×C4×D149 | semidirect |
| 217. C2 | #23749712 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558725 | 2 |
| C2×#18011876 | 2 |
| C2×#18011873 | 2 |
| #23749712 | 2 |
| C2×#18011834 | 2 |
| C2×#18011831 | 2 |
| C2×C8×Dic149 | 2 |
| C2×#106×C149 | 2 |
| C2×C4×SD16 | 149 |