Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
456 conjugacy classes of subgroups; only the 152 normal subgroups are shown.
This group has 456 conjugacy classes of subgroups — too many to draw. Only its 152 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. #23750576 | C2 | semidirect |
| 3. #23750574 | C2 | semidirect |
| 5. #23750571 | C2 | semidirect |
| 6. #23750570 | C2 | semidirect |
| 18. #18011906 | C4 | semidirect |
| 19. #18011905 | C4 | semidirect |
| 20. #18011904 | C4 | semidirect |
| 24. #126×C149 | C4 | semidirect |
| 38. C4⋊Dic149 | C2×C4 | semidirect |
| 39. #14558715 | C2×C4 | semidirect |
| 40. #14558715 | C2×C4 | semidirect |
| 44. C4×Dic149 | C2×C4 | semidirect |
| 45. C4⋊C4×C149 | C2×C4 | semidirect |
| 47. C42×C149 | C2×C4 | semidirect |
| 89. C149 | #2383 | semidirect |
| 102. #126 | #10597010 | semidirect |
| 129. C4⋊C4 | C2×#10597010 | semidirect |
| 137. C42 | C2×#10597010 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #23750576 | 2 |
| #23750575 | 2 |
| #23750574 | 2 |
| #23750572 | 2 |
| #23750571 | 2 |
| #23750570 | 2 |
| #126×D149 | 2 |
| #2383 | 149 |