Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
410 conjugacy classes of subgroups; only the 121 normal subgroups are shown.
This group has 410 conjugacy classes of subgroups — too many to draw. Only its 121 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×#18012727 | C2 | semidirect |
| 2. #23752594 | C2 | semidirect |
| 3. #23752569 | C2 | semidirect |
| 4. #23752434 | C2 | semidirect |
| 5. #23752427 | C2 | semidirect |
| 6. #23752367 | C2 | semidirect |
| 7. #23752362 | C2 | semidirect |
| 8. #23752350 | C2 | semidirect |
| 10. #23752265 | C2 | semidirect |
| 11. #529×C151 | C2 | semidirect |
| 14. C2×#14558994 | C22 | semidirect |
| 15. C2×#14558992 | C22 | semidirect |
| 24. C4⋊(C151⋊C8) | C22 | semidirect |
| 25. #18012662 | C22 | semidirect |
| 26. #18012662 | C22 | semidirect |
| 31. C4×C151⋊C8 | C22 | semidirect |
| 33. #125×C151 | C22 | semidirect |
| 34. #124×C151 | C22 | semidirect |
| 38. C4×Q8×C151 | C22 | semidirect |
| 40. C4×D4×C151 | C22 | semidirect |
| 143. C151 | #3211 | semidirect |
| 145. #529 | D151 | semidirect |
| 163. #125 | C2×D151 | semidirect |
| 168. #124 | C2×D151 | semidirect |
| 172. C4×Q8 | C2×D151 | semidirect |
| 174. C4×D4 | C2×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012727 | 2 |
| #23752594 | 2 |
| #23752569 | 2 |
| #23752434 | 2 |
| #23752427 | 2 |
| #23752367 | 2 |
| #23752362 | 2 |
| #23752350 | 2 |
| #23752345 | 2 |
| #23752265 | 2 |
| #529×C151 | 2 |
| #3211 | 151 |