Finite Group DatabasebetaFinite Group DatabasebetaOrder 19072.
612 conjugacy classes of subgroups; only the 170 normal subgroups are shown.
This group has 612 conjugacy classes of subgroups — too many to draw. Only its 170 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. C2×Q8×#10597010 | C2 | semidirect |
| 3. (C2×#10597010)⋊Q8 | C2 | semidirect |
| 5. #23750575 | C2 | semidirect |
| 6. #23750572 | C2 | semidirect |
| 7. #23750571 | C2 | semidirect |
| 8. #23750561 | C2 | semidirect |
| 27. #18011900 | C4 | semidirect |
| 28. #18011899 | C4 | semidirect |
| 29. #18011898 | C4 | semidirect |
| 30. #18011897 | C4 | semidirect |
| 33. #124×C149 | C4 | semidirect |
| 51. C2×Dic298 | C2×C4 | semidirect |
| 52. C2×Dic298 | C2×C4 | semidirect |
| 62. C22⋊Dic149 | C2×C4 | semidirect |
| 63. #14558713 | C2×C4 | semidirect |
| 64. #14558713 | C2×C4 | semidirect |
| 65. C4×Dic149 | C2×C4 | semidirect |
| 66. C4×Dic149 | C2×C4 | semidirect |
| 67. C2×Q8×C149 | C2×C4 | semidirect |
| 69. C22⋊C4×C149 | C2×C4 | semidirect |
| 70. C42×C149 | C2×C4 | semidirect |
| 138. C149 | #2326 | semidirect |
| 156. #124 | #10597010 | semidirect |
| 178. C2×Q8 | C2×#10597010 | semidirect |
| 203. C22⋊C4 | C2×#10597010 | semidirect |
| 209. C42 | C2×#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×D4×#10597010 | 2 |
| (C2×#10597010)⋊Q8 | 2 |
| #23750577 | 2 |
| #23750575 | 2 |
| #23750572 | 2 |
| #23750571 | 2 |
| #23750561 | 2 |
| #124×D149 | 2 |
| #2326 | 149 |