Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
544 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 544 conjugacy classes of subgroups — too many to draw. Only its 197 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×Q8×Dic151 | C2 | semidirect |
| 4. #23752315 | C2 | direct (N × H) |
| 5. C2×#18012672 | C2 | semidirect |
| 7. C2×#18012649 | C2 | semidirect |
| 8. C2×#103×C151 | C2 | semidirect |
| 11. C2×#14558991 | C4 | semidirect |
| 15. Q8×Dic151 | C22 | semidirect |
| 23. #18012672 | C22 | semidirect |
| 25. #18012649 | C22 | semidirect |
| 29. #103×C151 | C22 | semidirect |
| 40. #14558991 | C2×C4 | semidirect |
| 41. C2×C151⋊C8 | C2×C4 | semidirect |
| 52. C2×Q8×C151 | C2×C4 | semidirect |
| 75. C151⋊C8 | C22×C4 | semidirect |
| 79. Q8×C151 | C22×C4 | semidirect |
| 105. C2×C151 | #440 | semidirect |
| 110. C151 | C2×#440 | semidirect |
| 117. C2×#103 | D151 | semidirect |
| 138. #103 | C2×D151 | semidirect |
| 144. C2×Q8 | C4×D151 | semidirect |
| 179. Q8 | C2×C4×D151 | semidirect |
| 217. C2 | #23752315 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×#14558991 | 2 |
| C2×Q8×Dic151 | 2 |
| C2×#18012701 | 2 |
| #23752315 | 2 |
| C2×#18012672 | 2 |
| C2×#18012661 | 2 |
| C2×#18012649 | 2 |
| C2×#103×C151 | 2 |
| C2×#440 | 151 |