Finite Group DatabasebetaFinite Group DatabasebetaOrder 19328.
392 conjugacy classes of subgroups; only the 125 normal subgroups are shown.
This group has 392 conjugacy classes of subgroups — too many to draw. Only its 125 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. Q8×Dic302 | C2 | semidirect |
| 3. #23752558 | C2 | semidirect |
| 4. #23752557 | C2 | semidirect |
| 5. #23752503 | C2 | semidirect |
| 6. #23752500 | C2 | semidirect |
| 7. #23752410 | C2 | semidirect |
| 8. #23752336 | C2 | semidirect |
| 9. SD16×Dic151 | C2 | semidirect |
| 10. C4×#14558991 | C2 | semidirect |
| 11. #460×C151 | C2 | semidirect |
| 77. Dic302 | SD16 | semidirect |
| 92. Q8×C151 | #41 | semidirect |
| 125. C151 | #3362 | semidirect |
| 134. #460 | D151 | semidirect |
| 206. Q8 | #14559003 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| Q8×Dic302 | 2 |
| #23752882 | 2 |
| #23752558 | 2 |
| #23752557 | 2 |
| #23752503 | 2 |
| #23752500 | 2 |
| #23752410 | 2 |
| #23752336 | 2 |
| SD16×Dic151 | 2 |
| C4×#14558991 | 2 |
| #460×C151 | 2 |
| #3362 | 151 |