Finite Group DatabasebetaFinite Group DatabasebetaOrder 1920.
364 conjugacy classes of subgroups; only the 101 normal subgroups are shown.
This group has 364 conjugacy classes of subgroups — too many to draw. Only its 101 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. #11752433 | C2 | semidirect |
| 2. D4×C3⋊#170 | C2 | semidirect |
| 4. D4⋊(C3⋊#170) | C2 | semidirect |
| 5. D4⋊(C3⋊#170) | C2 | semidirect |
| 6. #11746755 | C2 | semidirect |
| 7. #11746751 | C2 | semidirect |
| 79. C3×C5×D4 | M16 | semidirect |
| 93. C3⋊#170 | D8 | semidirect |
| 175. C5×D4 | #208 | semidirect |
| 217. C3×D4 | #704 | semidirect |
| 267. C3×C5 | #1581 | semidirect |
| 292. D4 | #6762 | semidirect |
| 314. C5 | #70879 | semidirect |
| 329. C3 | #10604793 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #11752433 | 2 |
| D4×C3⋊#170 | 2 |
| C3×D8×Dic5 | 2 |
| D4⋊(C3⋊#170) | 2 |
| #11746755 | 2 |
| #11746751 | 2 |
| #10604793 | 3 |
| #70879 | 5 |