Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
540 conjugacy classes of subgroups; only the 177 normal subgroups are shown.
This group has 540 conjugacy classes of subgroups — too many to draw. Only its 177 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. #23752116 | C2 | semidirect |
| 3. #23752104 | C2 | semidirect |
| 4. #23752101 | C2 | semidirect |
| 6. #23752086 | C2 | semidirect |
| 7. C4×C4⋊Dic151 | C2 | semidirect |
| 8. #23752059 | C2 | semidirect |
| 9. #383×C151 | C2 | semidirect |
| 13. #18012727 | C4 | semidirect |
| 34. C2×Dic302 | C2×C4 | semidirect |
| 48. (C2×D151)⋊C4 | C2×C4 | semidirect |
| 49. (C2×D151)⋊C4 | C2×C4 | semidirect |
| 58. C42×C151 | C2×C4 | semidirect |
| 118. C151 | #2337 | semidirect |
| 126. #383 | D151 | semidirect |
| 177. C42 | C4×D151 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#18012727 | 2 |
| #23752116 | 2 |
| #23752104 | 2 |
| #23752101 | 2 |
| #23752090 | 2 |
| #23752086 | 2 |
| C4×C4⋊Dic151 | 2 |
| #23752059 | 2 |
| #383×C151 | 2 |
| #2337 | 151 |