Finite Group DatabasebetaFinite Group DatabasebetaOrder 12224.
310 conjugacy classes of subgroups; only the 115 normal subgroups are shown.
This group has 310 conjugacy classes of subgroups — too many to draw. Only its 115 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
| subgroup | G/H | |
|---|---|---|
| center | C2×C4 | C22×D191 |
| commutator, socle, cosocle | C22×C191 | C24 |
| Frattini | C22 | C23×D191 |
| Fitting | C2×#41×C191 | C2 |
| hypercenter | C2×#41 | D191 |
| hypocenter | C191 | #532 |
| LCS | G ▷ C22×C191 ▷ C191 | |
| UCS | C1 ◁ C2×C4 ◁ C2×#41 | |
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C2×#15690287 | C2 | semidirect |
| 2. #20259320 | C2 | semidirect |
| 3. #20259318 | C2 | semidirect |
| 4. #20259311 | C2 | semidirect |
| 5. #20259309 | C2 | semidirect |
| 6. #20259294 | C2 | semidirect |
| 7. C4×C22⋊D191 | C2 | semidirect |
| 8. C2×C4×Dic191 | C2 | semidirect |
| 9. C2×#41×C191 | C2 | semidirect |
| 45. C2×C4×C191 | D4 | semidirect |
| 61. Dic191 | #41 | semidirect |
| 67. C191 | #532 | semidirect |
| 70. C2×#41 | D191 | semidirect |
| 113. C2×C4 | C22⋊D191 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#15690287 | 2 |
| #20259320 | 2 |
| #20259318 | 2 |
| #20259311 | 2 |
| #20259309 | 2 |
| #20259294 | 2 |
| C4×C22⋊D191 | 2 |
| C2×C4×Dic191 | 2 |
| C2×#41×C191 | 2 |
| #532 | 191 |