Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
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×#10597010 | C4 | semidirect |
| 17. #18011974 | C4 | semidirect |
| 23. #18011836 | C4 | semidirect |
| 24. #18011835 | C4 | semidirect |
| 25. #18011834 | C4 | semidirect |
| 26. #103×C149 | C4 | semidirect |
| 77. Dic298 | C42 | semidirect |
| 91. Q8×C149 | C42 | semidirect |
| 106. #10597010 | #103 | direct (N × H) |
| 122. C149 | C4×#103 | semidirect |
| 147. #103 | #10597010 | direct (N × H) |
| 189. Q8 | C4×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×Q8×#10597010 | 2 |
| C2×#18011974 | 2 |
| C2×C8×#10597010 | 2 |
| C4⋊C4×#10597010 | 2 |
| #23750499 | 2 |
| #23750498 | 2 |
| #103×D149 | 2 |
| C4×#103 | 149 |