Finite Group DatabasebetaFinite Group DatabasebetaOrder 384.
402 conjugacy classes of subgroups; only the 197 normal subgroups are shown.
This group has 402 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.
| subgroup | G/H | |
|---|---|---|
| center, Frattini | C2×C4 | C23×D3 |
| commutator, socle | C22×C3 | C23×C4 |
| Fitting, prime radical | C3×#525 | C2 |
| cosocle | C2×C3×C4 | C24 |
| hypercenter | #525 | D3 |
| hypocenter | C3 | #2978 |
| LCS | G ▷ C22×C3 ▷ C3 | |
| UCS | C1 ◁ C2×C4 ◁ #525 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #5234 | C2 | semidirect |
| 3. #5207 | C2 | semidirect |
| 4. #5012 | C2 | semidirect |
| 5. #5011 | C2 | semidirect |
| 6. #5000 | C2 | semidirect |
| 17. C2×#208 | C22 | semidirect |
| 18. C22×C3⋊C8 | C22 | semidirect |
| 22. #830 | C22 | semidirect |
| 23. C4⋊(C3⋊C8) | C22 | semidirect |
| 24. #803 | C22 | semidirect |
| 25. C4×C3⋊C8 | C22 | semidirect |
| 173. C3 | #2978 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C3×#525 | 2 |
| #5234 | 2 |
| #5207 | 2 |
| #5012 | 2 |
| #5011 | 2 |
| #5000 | 2 |
| #2978 | 3 |