Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
170 conjugacy classes of subgroups; only the 60 normal subgroups are shown.
This group has 170 conjugacy classes of subgroups — too many to draw. Only its 60 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center, socle | C2×C3 | #459 |
| commutator, Frattini, cosocle | C2×C8 | C23×C3 |
| LCS | G ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1 | |
| UCS | C1 ◁ C2×C3 ◁ C2×C3×C4 ◁ C3×C4×C8 ◁ G | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C3×#509 | C2 | semidirect |
| 2. C3×#493 | C2 | semidirect |
| 3. C3×#443 | C2 | semidirect |
| 4. C3×#364 | C2 | semidirect |
| 5. C3×#361 | C2 | semidirect |
| 6. #2213 | C3 | direct (N × H) |
| 18. #509 | C2×C3 | semidirect |
| 19. #493 | C2×C3 | semidirect |
| 20. #443 | C2×C3 | semidirect |
| 21. #364 | C2×C3 | semidirect |
| 22. #361 | C2×C3 | semidirect |
| 26. C3×Q16 | D4 | semidirect |
| 32. C3×D8 | D4 | semidirect |
| 69. Q16 | C3×D4 | semidirect |
| 75. D8 | C3×D4 | semidirect |
| 118. C3 | #2213 | direct (N × H) |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#509 | 2 |
| C3×#493 | 2 |
| C3×#443 | 2 |
| C3×#364 | 2 |
| C3×#361 | 2 |
| #2213 | 3 |