Finite Group DatabasebetaFinite Group DatabasebetaOrder 1152.
1416 conjugacy classes of subgroups; only the 254 normal subgroups are shown.
This group has 1416 conjugacy classes of subgroups — too many to draw. Only its 254 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C22×C4 | C22×D9 |
| commutator, cosocle | C23×C9 | C24 |
| Frattini, socle | C23×C3 | C23×D3 |
| Fitting | C22×C9×#41 | C2 |
| hypercenter | C22×#41 | D9 |
| hypocenter | C9 | #2388 |
| LCS | G ▷ C23×C9 ▷ C9 | |
| UCS | C1 ◁ C22×C4 ◁ C22×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C9×#41 | C2 | semidirect |
| 2. C2×C4×#611 | C2 | semidirect |
| 3. #10588911 | C2 | semidirect |
| 4. #10588910 | C2 | semidirect |
| 5. #10588903 | C2 | semidirect |
| 6. #10588902 | C2 | semidirect |
| 7. C4×#3676 | C2 | semidirect |
| 37. C22×C4×C9 | D4 | semidirect |
| 75. C22×D9 | #41 | semidirect |
| 88. C2×Dic9 | #41 | semidirect |
| 90. C22×#41 | D9 | semidirect |
| 191. C22×C4 | #611 | semidirect |
| 215. C9 | #2388 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C9×#41 | 2 |
| C2×C4×#611 | 2 |
| #10588911 | 2 |
| #10588910 | 2 |
| #10588903 | 2 |
| #10588902 | 2 |
| C4×#3676 | 2 |
| #84095 | 3 |